I want to make a mod for Among Us which will allow people to stay in game despite short-lived connection problems (as opposed to being kicked after 1 second of network issues).
Connection timeouts are usually handled server-sided, not client-sided. That means that this is a problem which should be fixed by the developers themselves. I have not read their sourcecode (and I can not), but I doubt that this is a particularly difficult code change to make on the server-side (but I could be mistaken - this is very hard to judge from the outside).
However, there could be a workaround which I have seen in different contexts where unreliable clients needed a reliable connection to a server: Develop a proxy server - an intermediate server which lets players connect and then connects to the actual server on their behalf. Program the proxy server that it will keep the connection to the actual server alive when the client is temporarily unreachable. Then deploy that server in a reliable location (like a datacenter) and modify the client to connect to the proxy instead of the actual server.
But as I said, this would be a lot of effort in both development and logistics compared to just letting the developers fix the problem.
You also can not expect such a jury-rigged solution to get much support from the developers. In a competitive multiplayer game, any client modification or anything which tabs into the connection between clients and server could be a potential cheat. I do not know how cheater-infested Among Us is already, but if it goes the route of any other suddenly popular game, it will soon be in desperate need of a stop-gap measure against a rampant cheating problem. There will be a myriad of different hacks and cheats ruining the game, and the developers will have to quick and efficient find a way to get rid of them. As an Among Us player, you should be familiar with the collateral damage caused by justified paranoia: If you act suspicious, you go out the airlock! The usual solution developers go to in such cases is to slap on a client-sided anti cheat tool which does its best to prevent any kind of client modification or connection shenanigans (including benign ones) and automatically bans the players who use them.
So tl;dr: Your best strategy as a player to solve this problem for the community is to keep complaining to the developers until they fix it. (and then to thank them after they fixed it. We are all humans, you know. It's good for our motivation to hear that we did something right once in a while.)
Short answer: No
Theoretically you could if you knew the networking protocals that are involved and managed to compile a compatible version of the game with your fixes and got everyone in the game to swap a few DLL files.
But realistically this is only something that the developer can do as they are the ones that have the source code and control over the server infrastructure so thereby have the best overview of what the issues are and possible fixes for them. A normal person can't reasonably do this without getting into legal trouble and/or spending a lot of time decompiling the source and trying to recompile it in a way that makes the original game work without getting banned by the servers (if they have that capability).
Without the source code your out of luck, you could try emailing the developers to offer help in figuring out networking issues but I wouldn't get my hopes up that anything will happen as developers don't usually give away their games source to people outside the company/project.