Fighting Tyranids AND Tau?

[Zipline]

I've got a problem. My two usual opponents, Tyranids and Tau, use tactics that are diametrically opposed, and I cannot for the life of me find a list that deals with both satisfactorily. I was running a melee-centric army for a long time but my friends adapted to it, and now it's not very effective. The sheer number of options and combinations in my codex are starting to give me a headache, too, so I figured I'd better ask for some help. First, what I own:

1x Kayvaan Shrike

1x SM Captain

25x Tactical Marines

5x Assault Marines

5x Scouts

5x Terminators (I bought a conversion kit to make them TH/SS Assault Termies if need be)

1x Dreadnought

1x Rhino

 

My Tyranid friend is giving me the most trouble. His usual list is usually something like two max squads of Genestealers, four Warriors, a whole mess of 'Ga(u)nts on foot, a Zoanthrope/Doom of Malantai (how is such a powerful unit only 90 pts?! It's unkillable!) in a Mycetic Spore, and a deathstar, which is typically something like the following:

1x Swarmlord/ Hive Tyrant w/ lash whip and bone swords

3x Tyrant Guard w/ last whip and bone swords

1x Tyranid prime with bone swords

 

I recently ran a deathstar of my own (Kayvaan, Captain w/ Relic Blade, Hellfire Rounds, Digital Weapons, and a jump pack, and 5 Assault Marines w/ Sergeant w/ Lightning Claw and SS) against his, and beyond Kayvaan killing the Tyranid Prime, it was like flying into a “brick wall.” As for my Tau friend, I usually see three squads of two Crisis Suits w/ various configurations, 2-3 Railheads, and a mess of Fire Warriors. He's also debating switching to IG in the future, but that's not a concern for at least half a year.

 

So what do you think, guys? Can you give me any tips on 1,500 pt lists using the units I have here? I suppose it doesn't have to be a single list to deal with both at the same time, but the convenience of that would be nice. I am willing to proxy, and if necessary I can spend at most $100 USD on new units. In particular I've been running tests with a pair of Predators (AC/HB and LC/LC), but they didn't seem to perform very well. Whirlwinds don't seem to have the punch to handle deathstars, and Vindicators are prone to blowing themselves up with their short range and scatter. A Land Raider would be nice, but 250 points for a glorified taxi is such a huge risk, I don't know if I'm willing to take it, especially with three Hammerheads on the table at a time. Anyway, thanks for reading and I'm looking forward to your feedback.