So I have managed to get it past the bootup. I switched away from the LM317, which I realized was choking somehow under the power requirements and dropping voltage to 3.0v when the ESP was connected.
Now it seems I am getting somewhere. Booting at 74880bps, I get the following:
Code: Select all ets Jan 8 2013,rst cause:2, boot mode:(3,6)
load 0x40100000, len 816, room 16
tail 0
chksum 0x8d
load 0x3ffe8000, len 788, room 8
tail 12
chksum 0xcf
ho 0 tail 12 room 4
load 0x3ffe8314, len 288, room 12
tail 4
chksum 0xcf
csum 0xcf
2nd boot version : 1.2
SPI Speed : 40MHz
SPI Mode : QIO
SPI Flash Size : 4Mbit
jump to run user1
Very promising! Next, booting at 115,200bps, I can see the ready prompt:
Code: Select allAi-Thinker Technology Co. Ltd.
ready
However it is still deaf to TX from the terminal of any kind. So close, yet so far.
UPDATE: Got an "OK" from the system after reflowing the solder joints yet again. I suspected it may be a cold solder but since I had revisited it and checked continuity a few times I was doubtful. Turns out that was definitely the issue. Onwards!