Re-designing Speakers from the 70s (Sansui SP 1700)

Having a measurement microphone and REW is a good start for a project like this. Otherwise you're completely "flying blind". A large amount of outside space tends to be useful for taking speaker measurements, too (see why).

Nobody builds speakers with deeply recessed baffles any more, and for good reason - the edges cause lots of trouble with early reflections (combing / diffraction). This speaker has not one but two sets of recesses (plus a grille of unknown influence - their frames tend to be an issue), moreover the outer edge would be extremely hard to get rid of if the speaker's appearance is not to be changed. Modern speakers are looking way different these days, and they very much have to. (You could hardly get more different than some Genelec Ones, although to be fair something like a Neumann KH420 would probably be a much better comparison point.)

BTW, I would estimate that a complete redesign may easily require as much skill and effort as building from scratch.

Oh, and I know you're quite aware of it, but that placement really does suck bigtime. It's pretty much a worst case WRT symmetry, soundstaging must be all over the place unless you've got some super thick curtains and room EQ, both of which I very much suggest you look into. And yes, with one speaker shoved right in the corner big bass is not a surprise - that's about 1/8 space or a +9 dB boost from boundary gain if I'm not mistaken. I hope it's at least toed in substantially to face away from the problematic window front. In this case you may want to have the speaker axis cross in front of the listening position.

The measured response suggests some of the speaker's known eccentricities coming through in the upper mids and highs. Where was this measured? Use windowing to get a better look at mid/highs performance (down to just a few ms). An omni measurement mic at the listening position will pick up way more room reverb than your hearing would, so do move closer if need be. The crux is that the disagreement between hearing and measurement tends to diverge if the speakers have uneven dispersion, which I suspect these do (next to badly suppressed driver breakup).

How are room acoustics right now? Is the room lively with lots of hard surfaces, or filled with carpets and furniture and stuff?

Here's some reading material for ya. They've got a YT channel as well.
 
The bass is .....
Please don´t fully quote the post that´s just above your answer.
Thanks.

as of:
In the attachments are pictures of the elastic surrounds, they look really gleamy, as if they're dipped in Tar. they're not disintegrating and they're still somewhat elastic (bounce back when lightly pushed with fingers).

Do you recommend that i replace the elastic surrounds?
No, unless disintegrating, which is not the case.