The PCE/TG16 is a seldom hacked console and I am not sure how many around here, or indeed in general, hack the console with an eye to ROM hacking style hacks, I certainly am not one that does anything there; indeed the only things I have ever really played of the libraries are the awesome versions of bomberman it has (genesis/megadrive and SNES bomberman and then some is the usual description) and a go on the castlevania to say I have- I have not even sampled the supposedly awesome library of shmups it has.
Older consoles compression then.... the 77 in LZ77 refers to the year it was cooked up so pretty much any compression you would have read about as part of ROM hacking is viable, however what I have seen of consoles of this vintage says they usually opt for the low end compression methods like RLE and the dual tile encoding although fairly primitive (which is not to say easy to work with, decode by hand or handle in general) LZ/LZSS and Huffman are certainly available. My lack of PCE/TG16 knowledge will betray me once more as I can not even tell you if whatever passed for the SDK had something (or a primitive version of zlib got a port) or if the PCE BIOS had functions in it, indeed anything I say will be the result of a search along the lines of "PCE BIOS functions list" so I will not even pretend.
I can however link up my present favourite document in the introduction to compression stakes, https://ece.uwaterloo.ca/~ece611/LempelZiv.pdf
. Although it is mainly about LZ (although not an exhaustive work it could certainly be the basis for one) it covers the likes of RLE and Huffman quite well.
I did however come here mainly to say have you tried corruption? I can talk in broad terms about compression methods and possibilities at some length but having an example of the would be section. To that end if you can corrupt the ROM image until the section you want breaks and then figure out where it is that is a far nicer starting point. Do try to make sure you have not just caused a crash at the right time, though figuring out what is a crash and what is corruption is part of the trick to the method I guess.
That said compression and text rendered as graphics at compile time are two of the three usual suspects for this so do carry on with this line of logic; the third, especially as far as title screens and intro sequences are concerned, is that it is a different encoding to the rest of the game.