SC2Mapster

Nope. There's nothing special you need to do, for your map to work correctly in Battle.net. The behavior you experience is either caused by some obscure bug in SC2 which reason I cannot guess. Or there's *something* in your map that causes this freeze.

It's good that you were able to save the replay. And what's better, it seems like the bug can be reproduced by running the replay.
If you could attach the replay here, or upload it somewhere and post the link, then I'd look into it myself (yes, replay from online game is all I need). If the bug will also occur on my end, I should be able to track down the cause.
Also, what's the length of the replay? Because if the freeze actually happens right after start, I'd expect it to have ~0s.

In the meantime, here's small checklist you could do, to narrow the area. Proceed it until you'll confirm the freeze doesn't happen anymore.
(Of course before doing anything of this, backup your map.)
- Simply republish the map w/o changing anything. To make sure this is not result of some error during publishing process.

- Remove custom dependencies/mods (if you have any). Publish & retry.
- Remove triggers that are running at the start of the game. Publish & retry.
- Remove ALL of the triggers. Publish & retry.
- Remove ALL preplaced units on the map. Publish & retry.
If at this point the freeze will still be occuring, I'll be suprised. But you should keep going and remove remaining things such as: custom imported assets (if you have any), lobby attributes/variants, data entries.. it might sound funny, but I'm serious - when you can't guess the source of your trouble, then removing the possibilities piece by piece is smart way to approach it.
Unless you'll end up with empty map, haha.

Given the fact it works flawless in test mode, it does seem pretty weird.

I could see infinite loop in triggers or infinite recursion in Data causing something like this, where game freezes for a while thus putting you in a state of being not available to Battle.net. Although in such scenario it should unlock after a while - when SC2 detects things went wrong, to put it simple.

But.. if you can't reproduce it offline in test mode, I don't think that's the problem you're running into.

Does the disconnect happen every time? Are you able to quit the game before getting "attempting to reconnect" screen pop up, and have a score screen visible? Does the replay file save after the game?

Quick recap about Star Battle for these unaware about state of the game:

The original map developer (@zedu) abandoned project years ago (around 2014). Since then many community forks appeared.

To my knowledge @zedu didin't pass original map files to anyone, thus none of these forks can be considered official. They all pulled map files from bnet. Aside from that the main map file had obfuscated map script (deeply obfuscated, not the light version sc2 editor generates) - without Triggers scheme. Thus they struggled to edit game beyond Data section. Luckly though, some of the game code was in dependency mods which were untouched (publshed as "unlocked" to arcade).

Anyway, problem was that every author of that fork had its own vision on the game and its balance. What leaded to conflicts and final split of the community. Where both EU and NA had it's own game copy. And were developed independently.
(There were also minor forks, from other people. But they did not get much attention.)

EU dev gave up on it very quickly. Even though his version is still the one being played the most on EU (Star Battle 3.1).

Then we have NA.. their dev team had one guy which was preparing complete overhaul of game mechanics (could call it 4.0) for several months, where he finally gave up because community explicitly said it was not what they wanted.

This was around 2016, where I stopped folling it.

I seriously wonder if it is even worth to attempt ressurecting this game at this point. Given the fact that community is not known to be very friendly.

I'm somewhat familiar with Star Battle code, thus I'm capable of helping you. But since you show the attude of "Hey, come and do *this* thing for me", instead of "Hey, here's my problem and neccesery details. Help me solve it." I don't know if it's worth it. It might very likely end up being just another dead fork no one plays.

Do you have any communnity representatives supporting your endeavor? Where is community settled now? Since every SB forum I've used to visit is now dead.

As to your problem.. because you didn't provide necessary details, I can only guess. So here it is: 
Does your map you have Trigger Scheme file? (When you go to the Triggers section is it all blank?)
If it is blank, go to editor options, and check if you've enabled option "Obfsucare map script file" (I think it's in the Publishing tab).

If the above is correct, then upon publishing editor attempts to obfuscate the map script, but fails to do so, because the original triggers scheme is not present. And you end up with blank MapScript.galaxy file, which had overriden previous version that contained all core code needed for map too intialize properly.

Oh my God, you found the source of the bug. I almost can't  believe it :D

THANK YOU!!! If you happen to visit Warsaw or if we meet anywhere else by chance you're getting a vodka (or whatever else you drink) from me xD

How the hell did you figure out that it was the frame? Did you like run the map just in code,  matrix style, or something?

Honestly, I have no idea why I had that frame up. I must have added it while adding other loading screen stuff cause it sounded cool or something :D

"BattleUI? Like Battle.net? Gee, can't go wrong with that, right?" xD Fuuuuuuuu... Those kinds of bugs are the worst.Tiny stuff that you think only adds a little particle there, a semi-colon there. Ends up crashing your stuff.

As for the Allied Commanders. Good thing it wasn't that cause I am actually using some stuff from there :D

Damn, what else can I say. I'll keep testing it out properly now. You saved my life xD Thanks again.