Oh and I knew there was something faintly relevant to this: for extra cash there are mobile SIM bonding devices out there. Sky use them to aggregate ~8 SIMs (so that's 3g and 4g on o2/voda/three/ee) and stream HD video back to base:
Ok ok ok, that's probably way more expensive than you were thinking, but it shows that this sort of thing is possible to aggregate the bandwidth between providers.
Otherwise, once you've built up your list of the providers which are fast enough where you'll be needing them, just give their business sales a ring and see what they can do. The current EE 100GB sims, plus Three's unlimited 4G-on-handset might serve as a faintly useful bargaining chip.