Here's my soft start circuit. Thanks for suggestions from Tilmann and Jeroen.
The idea is to drive the ends of the transformer with in-phase square waves and then slowly walk them to 180 degrees, to achieve a soft start. An FPGA can do that easily. We might take a second... but that would simulate forever.
What works well is to use two spice "modulator" elements and FM the frequency of one of them for 50 ms, until they are 180 degrees out of phase.
Spice BV elements with sin(time*freq) type expressions seemed to overload or something.
Version 4 SHEET 1 2568 1220 WIRE -512 -944 -576 -944 WIRE -400 -944 -512 -944 WIRE 16 -944 -32 -944 WIRE 48 -944 16 -944 WIRE 256 -944 192 -944 WIRE 304 -944 256 -944 WIRE -1104 -912 -1136 -912 WIRE -1040 -912 -1104 -912 WIRE -400 -912 -400 -944 WIRE -32 -912 -32 -944 WIRE 192 -912 192 -944 WIRE -128 -896 -144 -896 WIRE -80 -896 -128 -896 WIRE -848 -880 -896 -880 WIRE -800 -880 -848 -880 WIRE -128 -848 -144 -848 WIRE -80 -848 -128 -848 WIRE -576 -816 -576 -944 WIRE -784 -800 -848 -800 WIRE -720 -800 -784 -800 WIRE -624 -800 -720 -800 WIRE -400 -800 -400 -832 WIRE -32 -800 -32 -832 WIRE 192 -800 192 -832 WIRE -848 -768 -848 -800 WIRE -624 -752 -656 -752 WIRE -576 -688 -576 -736 WIRE -448 -688 -576 -688 WIRE -368 -688 -448 -688 WIRE -208 -688 -304 -688 WIRE 160 -688 -32 -688 WIRE 208 -688 160 -688 WIRE 416 -688 272 -688 WIRE 480 -688 416 -688 WIRE 544 -688 480 -688 WIRE 656 -688 544 -688 WIRE -848 -656 -848 -688 WIRE -576 -640 -576 -688 WIRE -656 -624 -656 -752 WIRE -624 -624 -656 -624 WIRE -720 -576 -720 -800 WIRE -624 -576 -720 -576 WIRE 208 -576 112 -576 WIRE 416 -576 416 -688 WIRE 416 -576 272 -576 WIRE -1024 -560 -1104 -560 WIRE -880 -560 -944 -560 WIRE -848 -560 -880 -560 WIRE -1104 -544 -1104 -560 WIRE -848 -544 -848 -560 WIRE -656 -528 -656 -624 WIRE -576 -528 -576 -560 WIRE -208 -528 -208 -688 WIRE -32 -528 -32 -688 WIRE 416 -512 416 -576 WIRE 544 -512 544 -688 WIRE 656 -512 656 -688 WIRE -1104 -448 -1104 -464 WIRE -848 -448 -848 -480 WIRE -528 -400 -576 -400 WIRE -480 -400 -528 -400 WIRE -576 -368 -576 -400 WIRE 160 -368 160 -688 WIRE 208 -368 160 -368 WIRE 416 -368 416 -448 WIRE 416 -368 272 -368 WIRE -784 -352 -848 -352 WIRE -720 -352 -784 -352 WIRE -624 -352 -720 -352 WIRE -848 -320 -848 -352 WIRE -624 -304 -656 -304 WIRE -576 -240 -576 -288 WIRE -448 -240 -576 -240 WIRE -368 -240 -448 -240 WIRE -208 -240 -208 -448 WIRE -208 -240 -304 -240 WIRE -32 -240 -32 -448 WIRE 112 -240 112 -576 WIRE 112 -240 -32 -240 WIRE 208 -240 112 -240 WIRE 416 -240 416 -368 WIRE 416 -240 272 -240 WIRE 544 -240 544 -432 WIRE 544 -240 416 -240 WIRE 656 -240 656 -432 WIRE 656 -240 544 -240 WIRE -848 -208 -848 -240 WIRE -576 -192 -576 -240 WIRE 416 -192 416 -240 WIRE -656 -176 -656 -304 WIRE -624 -176 -656 -176 WIRE -1072 -160 -1152 -160 WIRE -880 -128 -928 -128 WIRE -848 -128 -880 -128 WIRE -720 -128 -720 -352 WIRE -624 -128 -720 -128 WIRE -1152 -112 -1152 -160 WIRE -656 -80 -656 -176 WIRE -576 -80 -576 -112 FLAG -400 -800 0 FLAG -512 -944 +48 FLAG -32 -800 0 FLAG -128 -896 HA FLAG -128 -848 HB FLAG 16 -944 BRO FLAG -448 -688 HA FLAG -448 -240 HB FLAG -576 -528 0 FLAG -656 -528 0 FLAG -576 -80 0 FLAG -528 -400 +48 FLAG -656 -80 0 FLAG 416 -192 0 FLAG 480 -688 OUT FLAG -784 -800 A FLAG 256 -944 SS FLAG 192 -800 0 FLAG -1104 -912 SS FLAG -1152 -112 0 FLAG -784 -352 B FLAG -1104 -448 0 FLAG -880 -560 AB FLAG -848 -448 0 FLAG -848 -208 0 FLAG -880 -128 K FLAG -848 -656 0 FLAG -848 -880 J SYMBOL voltage -400 -928 R0 WINDOW 0 53 46 Left 2 WINDOW 3 53 78 Left 2 SYMATTR InstName V3 SYMATTR Value 48 SYMBOL e -32 -928 R0 WINDOW 0 45 50 Left 2 WINDOW 3 49 78 Left 2 SYMATTR InstName E5 SYMATTR Value 1 SYMBOL sw -576 -720 M180 WINDOW 0 58 74 Left 2 WINDOW 3 61 47 Left 2 SYMATTR InstName S2 SYMATTR Value Sj SYMBOL sw -576 -544 M180 WINDOW 0 58 74 Left 2 WINDOW 3 61 47 Left 2 SYMATTR InstName S3 SYMATTR Value Sj SYMBOL sw -576 -272 M180 WINDOW 0 58 74 Left 2 WINDOW 3 61 47 Left 2 SYMATTR InstName S4 SYMATTR Value Sj SYMBOL sw -576 -96 M180 WINDOW 0 58 74 Left 2 WINDOW 3 61 47 Left 2 SYMATTR InstName S5 SYMATTR Value Sj SYMBOL cap -304 -704 R90 WINDOW 0 79 30 VBottom 2 WINDOW 3 86 29 VTop 2 SYMATTR InstName C1 SYMATTR Value 20µ SYMBOL FerriteBead -336 -240 R90 WINDOW 0 -37 -1 VBottom 2 SYMATTR InstName L1 SYMATTR Value 2.5µ SYMATTR SpiceLine Ipk=3 Rser=0.0023 Rpar=475 Cpar=1.75p SYMBOL ind2 -224 -544 R0 WINDOW 0 -49 37 Left 2 WINDOW 3 -61 76 Left 2 SYMATTR InstName L2 SYMATTR Value 72µ SYMATTR Type ind SYMBOL ind2 -48 -544 R0 WINDOW 0 61 40 Left 2 WINDOW 3 50 76 Left 2 SYMATTR InstName L3 SYMATTR Value 112µ SYMATTR Type ind SYMBOL schottky 208 -672 R270 WINDOW 0 42 40 VTop 2 WINDOW 3 -14 54 VBottom 2 SYMATTR InstName D1 SYMATTR Value RB168VAM150 SYMATTR Description Diode SYMATTR Type diode SYMBOL cap 400 -512 R0 WINDOW 0 -58 36 Left 2 WINDOW 3 -70 67 Left 2 SYMATTR InstName C6 SYMATTR Value 100µ SYMBOL res 528 -528 R0 WINDOW 0 -63 51 Left 2 WINDOW 3 -61 83 Left 2 SYMATTR InstName R5 SYMATTR Value 5K SYMBOL schottky 208 -560 R270 WINDOW 0 39 33 VTop 2 WINDOW 3 -14 55 VBottom 2 SYMATTR InstName D2 SYMATTR Value RB168VAM150 SYMATTR Description Diode SYMATTR Type diode SYMBOL schottky 272 -384 R90 WINDOW 0 -10 31 VBottom 2 WINDOW 3 45 28 VTop 2 SYMATTR InstName D3 SYMATTR Value RB168VAM150 SYMATTR Description Diode SYMATTR Type diode SYMBOL schottky 272 -256 R90 WINDOW 0 -16 31 VBottom 2 WINDOW 3 43 32 VTop 2 SYMATTR InstName D4 SYMATTR Value RB168VAM150 SYMATTR Description Diode SYMATTR Type diode SYMBOL current 656 -512 R0 WINDOW 0 54 63 Left 2 WINDOW 3 19 107 Left 2 WINDOW 123 0 0 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName I1 SYMATTR Value PULSE(0 0.5 75m 1m 0 9) SYMBOL voltage 192 -928 R0 WINDOW 0 58 36 Left 2 WINDOW 3 41 74 Left 2 WINDOW 123 0 0 Left 0 WINDOW 39 0 0 Left 0 SYMATTR InstName V1 SYMATTR Value PULSE(0 1 0 1u 1u 50m) SYMBOL SpecialFunctions\\modulate -1040 -912 R0 WINDOW 0 56 29 Left 2 SYMATTR InstName A1 SYMATTR SpiceLine space=250K SYMATTR SpiceLine2 mark=250.01K SYMBOL SpecialFunctions\\modulate -1072 -160 R0 WINDOW 0 56 31 Left 2 SYMATTR InstName A2 SYMATTR SpiceLine space=250K SYMATTR SpiceLine2 mark=250K SYMBOL bv -1104 -560 R0 WINDOW 0 46 98 Left 2 WINDOW 3 30 135 Left 2 SYMATTR InstName B1 SYMATTR Value V=V(A) * V(B) SYMBOL res -928 -576 R90 WINDOW 0 66 56 VBottom 2 WINDOW 3 65 57 VTop 2 SYMATTR InstName R1 SYMATTR Value 1K SYMBOL bv -848 -336 R0 WINDOW 0 -89 48 Left 2 WINDOW 3 -185 94 Left 2 SYMATTR InstName B2 SYMATTR Value V=sgn(V(K)) SYMBOL bv -848 -784 R0 WINDOW 0 -89 59 Left 2 WINDOW 3 -183 96 Left 2 SYMATTR InstName B3 SYMATTR Value V=sgn(V(J)) SYMBOL cap -864 -544 R0 WINDOW 0 -53 40 Left 2 WINDOW 3 -66 68 Left 2 SYMATTR InstName C2 SYMATTR Value 100n TEXT 216 -136 Left 4 ;P970 DC-DC Converter TEXT 288 -88 Left 3 ;JL Jan 15 2025 TEXT -200 -80 Left 2 !.model Sj SW(Ron=50m Roff=1g) TEXT -200 -128 Left 2 !.tran 0 100m 0 20n TEXT -192 -568 Left 2 ;PL300-101L TEXT -160 -488 Left 2 ;4T TEXT -96 -488 Left 2 ;5T TEXT -200 -720 Left 2 !K1 L2 L3 0.999 TEXT -392 -192 Left 2 ;163-5001 TEXT -392 -152 Left 2 ;2.7 uH 5A TEXT -168 -600 Left 2 ;Coilcraft TEXT 232 -816 Left 2 ;50 ms soft start