You can get a little idea of what I have from this photo, though it's hard to find everything unless you know where to look
LPC Link2 / LPC4370 triple core
QorIQ Power Architecture
Just about everything under the sun (too much to list individually)...
All kinds of Tiny, Mega, Xmega, and Arduino boards
various XMEGA / Xplained boards
ATSAM9 ARM9 SoC
A few Spartan3 dev boards
A pack of old XC9572 CPLDs
Olimex ICE40HX1K boards
LCMXO2280C-B-EVN (MachXO CPLD)
I've been collecting for a while
Actually I just came across the Blackice-II board and I think it is perfect for starting TI projects, minus the need for 5v<->3v level converters. It has an ICE40HX4K (actually unlocked to 8K with icestorm tools), an STM32L433 Cortex M4, SD card slot, and 512k (256k x 16) SRAM on-board. There's enough IO broken out to interface to the sidecar port. Wowza!
If I follow your TI replacement idea, you could marry your FPGA TI clone with Finalgrom99 and the tiny PEB and still have an expansion port for talking to real hardware like the speech synth or real disks. I think that would be really fun and take up a lot less space (aka portable and wife-friendly)
By the way, I was thinking about the weird problems you were having with your state machine and I wondered if you were registering the off-chip IO or not. If not, that could very easily explain the timing problems you were having and also why adding more states to ensure your critical control signals are set last could fix the problem. I had some similar issues with the memory controller part of a VGA controller I did back in college and registering the outputs made a world a difference in real-world behavior.