Taking the points one at a time:
Li+ / LiPoly have a voltage range of 4.2V (max) per cell [and that *is* max - got to be careful charging them] to 3V nom at discharge, so yes, you have to design to take account of the input range. They are fine to use [and I use them in my commercial products] provided you take care about their charge and discharge characteristics.
The LTC1735 is easily capable of controlling that current. if the IR parts are a little difficult for you then you could use a more common leaded part, but to handle the current (pulse current in the range of
15A or so for a 6A load) you may end up with SO-8 devices. (If you didn't look at the IRF6620/6623 yet, I'll note that the pads for source and gate are underneath the device, but my local proto person has no problem putting them down with a hot air gun).
To split things, then I would still use the LTC1735 (I have implemented
15A supplies with it), although Linear makes a nice range of controllers - I am just very familiar with it and it does the job quietly. The LTC1735 has a wide range of outputs (16V in max). If you are going to use it, then get SWCadIII from Linear and also read their excellent app notes. I suggest AN76 in particular, as it specifically targets the loop control structure used in the 1735.
On the note of splitting things up, you may also want to use a switcher. If so, because the current is lower here, you could use a device with the switch built in (you want efficiency, but you quickly get to a point of diminishing returns). For this, I'd personally use the LT1767-5. Pretrimmed so there's no divider feedback network, although you'll still need an inductor. 4.7uH works well, but if you need lower current than about 1.2A, you can use a smaller one (which will slightly raise the efficiency due to lower copper loss in the inductor).
On the other hand, you'll get about 75% efficiency with a LDO rated at
0.5A (Pd @ 0.5A = 250mW due to load, plus internal power consumption) if you drive it from 6V - not 83% due to the fact the internal circuitry has to be powered.
The LTC1767-5 has a typical efficiency of about 88% - 90% at that load for 8V-11V in.
Hope that all helps.
Cheers
PeteS