Regarding FRR. I like the delta option, provided it creates fixed rates (ie. they move only on the offer book). Computing variable frr+delta offers into frr could have funny effects.  

FRR isn't efficient because swap market is inefficient. Swap market is inefficient because it's impossible to speculate that the interest rate is going up. If I have a crystal ball that tells me rates are going up tomorrow, how can I act on that? I can't, at best I can stop lending and wait. Thus market stays inefficient. It's unrelated to the FRR, thus there's no fix to the FRR that can make it really better.

If I think rates are going down this works ok already.  

Possible solution:
Allow to reoffer borrowed (unused) swap, provided the swap time allows it (so if I got a 30 day swap I can lend it for 29 days).
In the case that the difference between rates is negative (ie. I borrowed swap for 30 days at 0.1%, I offer at 0.09% for 2 days) lock the difference for the whole maximum period. In addition to speculators who expect to make the difference later, this allows traders to reserve good (in their opinion) long term rates cheaper, at the additional cost of being locked for 2 days max (or other period they choose).  

This should decrease rates volatility, especially 1% spikes. At very high rates some traders might even close their longs to relend their swaps.