So, there are two main ideas I'm going to state in this one, and you can decide which one you prefer and want to use. The ideas aren't too different from each other, except for the base concept, so I'll just explain them in this paragraph. The first idea is for Shirou, Rin, Artoria, Archer, and maybe Lancer to all get transported to the world of DxD via Zelretch, post UBW. The second idea is for Illyasviel alone to get transported to the world of DxD, alongside maybe Shirou, and she/they summon heroic spirits from Fate/stay night. This should take place either after the Fate route or Heaven's Feel. I'll go more into detail in the following paragraphs, but one of the main differences is whether you want Shirou, Rin, and the others to be the main cast, or for Shirou, Illya, and the others to be the main cast.
Everyone should have a major power boost from entering the world of Highschool DxD, since it's in the age of gods, but I'm going to particularly focus on Archer. I want Archer's traced copies to last indefinitely and become their real counterparts in terms of strength and legend and all. This is because in the world of Highschool DxD, there is much more abundant mana and the world is still in the age of gods. Archer should still not be able to trace divine weapons, and he should also not be able to trace sacred gears, since they were created by God. I want Archer to be freed from his contract with Alaya, but still retain the power he gains from Alaya.
(From here on, I'll just be writing about the first idea. The second one you can do whatever you want with, since if I focused on that too, this idea might get too long, when I want this one to not reach the thousand words that sometimes ends up happening on these ideas. You are free to take ideas from the first idea and insert them into the second idea, however.)
Following our cast having been transported to the world of Highschool DxD, everyone is left confused at how they got there. Shirou, Rin, (or Illya), and Artoria all brainstorm together to figure out where they've ended up, piecing together their situation over time, with minor input from Archer and Lancer.
Have Shirou still not get along with Archer, but have it so that Archer no longer holds any desire to kill him anymore. Don't create unnecessary friction between Archer and the other characters, and don't have Lancer and Archer constantly fighting. They only did that in Fate/stay night because of the holy grail war; Archer has no reason to fight Lancer in a story of this sort, even if Lancer may still want to fight him despite that.
Despite his minor input in the conversations relating to figuring things out, Archer should be the most proactive and willing-to-do-whatever-it-takes kind of person in terms of finding information. He should be the one to find the most information on what world they've entered, and relay it to the others. This doesn't mean he should be the one who discovers everything, however. Lancer can find stuff out by going to a supernatural pub by accident and listening in on conversations, and Rin and Saber can pick up tiny details from weird occurrences around Kuoh.
Archer and the others should then be interrupted by Zelretch, who gives them special evil pieces that turn people into fake servants, like Sasaki Kojirou, rather than devils. I say fake servants because, without a legend, noble phantasm, or anything of that sort, it'd be impossible for them to become real servants.
This does not mean they can't become real servants however, and this is made easier by the fact that Archer can just give people their own noble phantasms from his collection.
To grow stronger as a servant, and become a real servant, one would still need to fight with their noble phantasm, and create their own legend with the weapon, however. Or alternatively, just have the people in the peerage use their own weapons and have those grow to be noble phantasms over time as the person's legend grows. I find that the alternative is far more appealing, but if you want to choose the first, I won't mind.
You should have Issei become a part of the peerage of servants, but anyone else's involvement is up to you.
I was going to add more to this chapter of ideas, but I’ve been working on this every now and then for around a week, and I can’t really figure out where to go from where I left off.