The thing about hops is that the only way you can maintain those pleasant aromatics is to keep them sealed and to refrigerate/freeze them. So your experiment would eliminate those two conditions.
Most hop extracts/oils I know are for adding bitterness to a beer. I don't know of (m)any that are for the aromatics because that is something that can't be easily processed due to their volatility. Again, application would be a problem, because even misting the concoction would result in an uneven distribution of the solution. That would be a big deal if you are talking about a potent and concentrated liquid.
Then you are faced with the foibles that adding moisture to a tobacco brings, namely mold. Hops have antibacterial properties but I don't think they can contend with mold...
By adding the dry hops to a tea bag, they will flake to dust somewhat as they dry and you are going to end up with a nice bit of hops plant matter in your tobacco jar even if the mesh is very fine. Hops is a relative to cannabis but I have heard from experimental folk that it is not as pleasant to smoke and has none of the psychoactive properties! :lol:
Lastly, I brought up the idea of immersing spices such as cloves/star anise into tobacco not long ago.
The general consensus was that there wouldn't be much of a flavour impact from that approach, even if you "steeped" them for months. The spices I mentioned are very hardy and their smells/flavours generally last for quite a long time. Hops on the other hand will fade EXTREMELY quickly and it won't take long for them to take on the unpleasant characteristics we have discussed.
So, honestly, it sounds hard to flavour tobacco with hops. You would likely have to buy more tobacco to experiment with dilution ratios for your vodka infusion, instead of using up your 'waste' tobacco - so the whole point would likely be eliminated.
The rum infusion on the other hand has been done many times as it is a traditional tobacco combination, with varying levels of success at the amateur level. I would say that is much easier to do but you will probably face combustion issues down the line with the addition of sugars and moisture. Time is probably your friend with an addition of rum to your tobacco.
Either way, I encourage you to experiment, I've just been giving you some straight talk about my thoughts on the matter. Let us know what you choose to do!