Am I asking for trouble pairing pro PA drivers with a tube amp?

Done a couple of two-ways on tube amps and the shouty thing is real but fixable. It usally comes down to the horn loading properly and how hot you run the compression driver. A shallow horn with a driver that doesn't like it will sound honky and hard right at the listening position. Two things help a lot: cross the tweeter over well above where the horn unloads, and pad the compression driver down so it sits level with the woofer. On soft valve gear people often set the balance a touch conservative anyway, your ears at lounge volume will thank you. If you can, pick a driver and horn combo known to play nice rather than mating any old cheap driver to whatever horn looks pretty, that mismatch is where the harshness comes from. On the port, low slot ports near a wall generaly behave better than you'd fear because the floor acts as an extension of the port, which can actually lower the effective tuning a bit. The risk is one-note bass if you tune it high hoping for output. Keep the tuning sensible for a 10 inch in a slim box, leave a hand's width between port and floor if you can, and it'll probably sound tidier than a rear port hard up against the wall. For the crossover, don't guess it. Get a cheap measurement mic and measure both drivers in the actual box, then model it in free software like VituixCAD before you solder anything. Start simple, second order on the woofer, and pad the tweeter to match. One thing that matters extra with valve amps: they often have a higher output impedance than a solid state amp, so dips in the speaker's impedance curve get accentuated and can sound lumpy. Keep the impedance fairly flat through the crossover region and you'll get a much friendlier result from that amp. One build note, hoop ply with knots near the edges can chip badly when you round over or route rabbets, so do all your edge work before final assembly and go slow on the knotty bits.

Not buying the bit about the floor extending the port and dropping the tuning. Tried a down-firing slot a few inches off a tiled floor in my old build and all it did was couple straight into the boundary and boom like mad untill I raised it and stuffed the slot. Close to a wall is worse again, the floor bounce cancels a chunk of the upper bass and you end up chasing it with the port. I'd mock the box up with a removable bottom panel first, sit it where it'll live, and only commit once you've listened. Cheap insurance compared to gluing a ply tower shut.

The hardwood face is the bit I'd think through before cutting anything. If you bond solid timber straight onto a ply baffle, the two move at different rates with the seasons and you can end up with a cracked or cupped face a year down the line. Veneer's much safer over a big flat area, and honestly big knots in veneer look great anyway. Also, with a shallow horn you're limited on how low you can cross the compression driver, so pick that driver first and work the woofer around it rather than the other way round. Ask me how I know on the wood movement one.

Following this one because my amp is a similar old thing and I keep eyeballing those big wooden speaker builds online too. The look is half the reason honestly, I want speakers my other half won't hide behind a plant. One thing I never got, is there a reason the big round driver goes above the little horn one instead of the other way round? It seems like the ear height one should be the horn, but every build I see does it the opposite way.

Update: raised the port a few inches off the floor and lightly stuffed the slot like you suggested, and the boom has mostly gone. Bass is way tighter now even backed near the wall. Still chewing on the hardwood face worry though, if solid timber glued to ply is likely to crack, would a thick veneer give me the same look without the risk?