Two points- I just tried a VGA extension cable, and it did _not_ work: the standard VGA extension (which is missing pin 13) won't do it. Blank display: checking the schematics from the service manual, all 15 pins are used. However, if you can find an extension that just wires all 15 pins straight through, it should work. Check before you buy.
Using the Studio 32 with the 1624 is very straightforward: you have 16 direct outs from the board, which go to the 16 track inputs (well, they do if you get an external 8-channel converter so that you can record 16 at once!), and you have 16 track outputs from the 1624 which go to the 16 tape returns. It's an inline board (with separate tape channel inputs), so no repatching was required for normal operations. The two were made for one another.
The Studio 24 is going to be a little harder to work with: you don't have a 1-1 mapping of track-to-channel. You only have 8 direct outs, but then the basic 1624 only has 8 actual input converters: the converter for input 1 can record onto track 1 or track 9. So half of your patching (the input side) is actually handled for you in the recorder: you can enable any input signal onto 2 tracks. That's how I handled the 1624 before I got my external converter (
the AC2496) so that I could track all 16.
The output side (monitoring and mixdown) will be something more of a pain. The Studio 24 was really meant for an 8-track project studio, so you'll be repatching and hacking around quite a lot. The good news is that many things you do really work as stereo pairs (stereo drum submixes, keyboard submixes, and so on). So I'd be tempted to develop a working style that let me use channels 1-8 as my hot recording channels, to tracks1-8. I'd set the track1-8 outputs up to
the channel1-8 tape returns. Tracks 9-16 I'd then set up on the four stereo inputs, and I'd submix, bounce, and then _move_ stereo pairs of tracks over on those real tracks to keep 1-8 available for tracking. The 1624 does digital track moves easily and cleanly- so you could bounce down to a pair, and then move them off to tracks15-16 to free up your primary 8 for further tracking.
The problem with the stereo input channels is that they don't have EQ, if I remember correctly. But they'll certainly work for you in the short term, and once you have a working style starting to develop, you'll probably find that you've outgrown that board.
I outgrew the Studio 32 pretty quickly, and moved on to a Soundcraft Ghost. However, I wasn't trying to learn an new working style- I was just redeveloping my old one from back in the day, and found that I really needed the flexibility that the Ghost gave me. I'm a lapsed large-format guy, anyway...
The Studio 24 is a little underpowered for a 16-track application. If you _can_ do the swap, I would do it: you're in for a lot of repatching, and doing more overhead/custodial work than you really need to, with the smaller board. I don't know about you, but that would detract from my productivity. Actaully, no- it'd _piss me off_. (;-) If you stay with the 24, get out the soldering iron and build a patchbay...