This is in part a frame challenge, although also providing a direct answer.
At the end, you sum up your question by asking how to approach the other band members about songs that fit "our intent". Before that, you say your drummer doesn't care too much about the songs you play, the other guitarist isn't able to judge the didactic value, and your bassist and singer are pushing for things with little didactic value.
Putting all that together, I find it hard to reconcile with asking them to play songs that fit "our intent" - you're asking them to pick songs that fit your intent.
You're very clear that your purpose with this band is to learn and develop as a musician. The other guitarist, who you initially started with, is also on board with that aim, but the impression I get from reading your post is that the drummer is indifferent and the other two members sound like they just want to have fun playing music they like. I think the key thing is for you to reconsider whether the make-up of this group is compatible with your goal of playing to develop particular musical skills. It may well be that the best way for you to achieve that goal is to just find a different group of people to play with - people who share that goal, or at least who are happy to actively help you work towards that goal.
If you don't want to do that, you can of course go ahead with your plan of asking the others to play things that better fit your intent. You said the drummer doesn't really mind what you play, and the other guitarist seems to share your goals (at least to a reasonable degree). So you only have the bassist and singer to convince.
You said they're your friends, and you didn't mention any personal issues coming from the disagreements over which songs to play, so I'd suggest you can be very straightforward. Something like:
"Hey, I've been enjoying playing with you, but some of the music that we've picked doesn't really fit with my goals. My main reason for being in the band is that I want to keep developing my [x,y,z] skills while school is shut over the summer. A lot of the [synth/pop/etc] we've been playing doesn't give me an opportunity to practise those skills. If I'm going to work on those things, I need to play more [blues/rock/whatever]. Would you be ok with us focusing the band in that direction?"
Don't talk about "the music you've suggested" not helping with your goals (it sounds accusatory and could lead to them getting defensive and arguing), and don't talk about "when I started the band" even if you did start it with those intentions (it could sound a little controlling and arrogant, even if you don't mean it to). Just explain the problem (the music you've been playing doesn't help you reach your goals), propose a solution (tell them what would be necessary to help you reach those goals), and ask if they're ok with it. Be prepared for the possibility that some of them might answer "no".
You say you've tried to speak to them before and they suggest writing your own arrangements of the songs they've suggested. That sounds like they're offering a compromise. You don't have to take that compromise (as I suggested above, you might just have to find other people to play with, either as well as or instead of your current group), but you should be prepared to explain why the compromise doesn't work for you (if you just bat away their suggested compromise without explaining why it doesn't help you, it could come across as you being rude and unreasonable). As above, they're your friends, so you can be quite straight-forward here: "I need to work on my [whatever] skills, composing new arrangements would take too much time away from that".
