I would need to refresh myself on my RF theory to be certain, and I am all for experimentation, but from my memory this is what I think would happen.
When you connect 2 antennas to 1 receiver, you will need a T connection, this will not double the dB of gain as you suggest, in theory it would reduce the gain, and the SWR will likely be high on the TX side of the house which is never good for the transmitter itself or good for the amount of power being transmitted. In the worst scenario it could blow your TX section on that port, at best it would effect both transmit and receive in a likely negative way. I think, based on what I know, that you would be much better off by putting good LHCP patches on 2 of the RX's and a good LHCP omni on the other 2, and I have seen people running 3 patches and only 1 Omni. I also would change the quad antennas too since that would actually give you more bang for the buck than the goggle side.
To be certain would require more information about the RX design and antenna priority scheme, for instance, is it 2 diversity receivers, and if so which antennas are paired (assuming both left and both right would be the pairs, but you know what happens when we assume), or is it 4 mono receivers and the composite video is from the strongest/best signal, or is it a rebuild composite of all the best qualities from all the signals (like the Rapidfire or Fusion RX's). It could also be a single receiver and it sees the 4 antennas as a "balanced tuned antenna array" (something your T connection from your idea would not do well given it is not balanced or tuned through antenna design or added circuitry). One thing is certain, DJI is pretty fat lipped about it, oh what I wouldn't give to talk to the lead RF, RX, and software design engineers on the project.
There is a lot to consider to actually "improve" your signal instead of hurting it, or possibly even your gear. While this is not scientific, you may want to watch and look for videos like this to see what is working for people and what you can learn about its design and operation. I would also look into the VAS Cyclops or the TrueRC or other reputable RF design manufacturers setups for the goggle side, since a bunch of smart guys with access at a high level to test equipment and insider knowledge about the DJI RF design, have already designed great "upgrades" and done the real science to see what works best.
Just my humble opinion sir...