I 1st worked with Z80s, so I'm familiar with that series. IIRC, the 3870 was Mosteks' version of the Z80. As such, it has no internal ROM of any kind... it predates that level of integration. I'd look for a (or several) 27xx chip(s) around it as the ROM/EPROM code storage. If it is the mask ROM version, you're right, extraction is impossible. You'll have to write a new controller/code to mime the behavior.
If 27xxs' are not damaged, they're fairly straightforward to read, but you'll need "old school" toys to do so. An EPROM programmer will read ROMs too. Good Hunting... <<<)))