A remake wouldn't add much info. The idea that DPP and HGSS took place at the same time is taken from the events in DPP itself, not HGSS.
You can freely trade between RBY and GSC as well. Of course, you can't trade new Pokémon and moves back to RBY, but you can trade back some stuff that didn't exist in RBY (such as Alakazam with the elemental punches). So (relatively) free trade is possible between games in different time frames. The only reason you can't do battle between RBY and GSC is the different game mechanics. Back then, it was explained through a time machine.
However, and this is a BIG however, you can still do free battle between RBY and GSC if you have a platform which supports both. This platform was called Pokémon Stadium 2 for the N64. In PS2, RBY cartridges could be used and then obeyed GSC mechanics in the game's battles.
BW and B2W2 don't have any different game mechanics. Two years have passed, but no moves nor Pokémon were added. This is why a "time machine" isn't necessary.
With regards to the RSE/FRLG thing, it's never stated that there is trade along different time frames. However, there is evidence that it can't be concomitant with DPP/HGSS, because the Orbs aren't in Hoenn during this period, and it can't be after BW either, since BW is after all the other games. This leaves the period between DPP/HGSS and BW, the period between FRLG and DPP/HGSS, or concomitant with FRLG. But how can you explain RSE being after DPP if none of the new evolutions discovered in Sinnoh are known to Hoenn locals?
3rd gen retconned a lot of things it shouldn't have, IMO. Because in 2nd gen it was made clear that the new Pokémon from Johto were discovered after the original 151, and the new types were a recent discovery as well. With 3rd gen, Johto Pokémon appear in Hoenn and the Sevii Islands, and the Steel-type is no longer unknown. RSE should've been placed after GSC, but as it stood, it was so detached from the other regions that it almost seems like it's from another dimension.
The plots are connected, because, where are all the Hoenn Pokémon coming from? They're caught during the plot of RSE and traded to the plot of FRLG, without any mention of time travel.
Also note that Marill, Azumarill, Slugma, Magcargo, Chinchou, Lanturn, Wynaut, Wobbuffet, Phanpy, Donphan, Natu, Xatu, Heracross, and Girafarig, among others(all of which were introduced in Gen II) happen to be native to Hoenn as well. Can we automatically write that off as just coincidence? I'm not using it as proof, because it really isn't either, but more as something to think over as well.
There are Johto Pokémon in Hoenn, just like there are Johto Pokémon in the Sevii Islands. Retcon of 2nd gen.
It's not all about how sinister the plans were, even though Aqua ans Magma chose thievery, etc. as well to accomplish what they wanted. The Grunt makes mention of how noticeable they made themselves and that being the downfall of their plans. Make of it as you wish, but Magma and Aqua made themselves well known as well.
Known only in Hoenn. And even in Hoenn, there are parts of the game where you don't see any mention of Aqua/Magma.
There's no mention of Aqua/Magma in further games of the series outside the grunts in Icirrus City, who live anonymously. If their actions were recent (as in only a few years ago) and relevant (as in worldwide relevant), there would be people in Unova discussing them in both BW and B2W2, much like there were people in both Johto and Kanto discussing Team Rocket's actions three years prior in HGSS.
Maxie was a reckless buffoon. Once he found out he couldn't control Groudon, he devised a stupid plan of stealing rocket fuel to cause an eruption in Mt. Chimney. It's one of the most senseless things I've seen a Pokémon villain do in the games, because it really had no reason, he wouldn't gain anything by doing it, and it certainly doesn't help the case of making people take Aqua/Magma more seriously.
Doesn't mean it's after Brawly became gym leader, but he was old and important enough to be taken under Bruno's wing. He doesn't look older than Bruno either. Bruno is an Elite Four member, it's assumed it takes hard work and recognition to reach such level. And time, of course.
This IMO is another proof that RSE is at the very least before DPP/HGSS because, if it was far into the future, Brawly would have to have been a kid when training under Bruno, who was a young adult in RBY. The NPC in FRLG references Brawly as a "guy", so, at least someone in his teens.
My evidence may not be all that strong, because, like I said, Hoenn seems to have happened in another dimension, but at least I'm not basing it in ifs, coulds and shoulds.