There's a lot to unpack in your question, so I'll try and address a few things.
As Barand already suggested, Ajax is the standard solution to this problem. Another possibility would be to use frames and have the lookup occur in an iframe. Without seeing your UI It's hard to understand the modality issue or possible solutions to it.
This sounds like a "you" problem. Using sessions does not require 1k lines of code or anything close to it.
If you have structure issues or something that doesn't work correctly, that probably relates to the structure (or lack thereof) in your code. One other issue that does sometimes crop up with manual regression testing, is that you can get into a situation where you are doing things that a normal user will never do, because you are repeatedly testing things with your browser which engages your local environment, making a session cookie and one or more sessions on the server.
Unit tests and automated testing tools are valuable in separating things, because they offer a fresh client environment and repeatability. With unit tests, you avoid environmental issues entirely.
If you are only able to do manual regression testing at this point, one suggestion I would make is that whenever you are doing testing, engage Incognito mode for that testing session and exit it when you're done.
From a usability point of view sessions offer a feature that you can't get with pure HTTP GET/POST, and that is server side storage of values that is both "secret" and persists as long as you want it to persist.
If someone accidently closes the browser or tab entirely, everything will be lost, whereas with sessions, they can get back exactly to the place they were.
So beyond the out-of-band issue you currently face, sessions can facilitate many usability features that can only otherwise be handled in any form with some combination of cookies and POST/GET variables. Of course Sessions do rely upon a session cookie, but that should be, once configured, completely invisible to you, whereas direct cookie handling requires a detailed understanding of HTTP and how/when cookies can be set.