I am aware that there is an inverse VIX ETF, but it is not leveraged. The only other way I can think of is to buy VXX puts? Is there another method I am not aware of that provides more leverage?
Puts are potentially pretty highly levered.
Another strategy would enter a delta neutral options position on a broad index like the S&P 500. Something like a short straddle. You can exit your positions when volatility falls. You don't have to wait until expiration.
If it were me, I would take a short position in a VIX futures contract (VX). These are offered by the CBOE. The margin requirements depend on which contract you are looking at, but they are not real large when compared with the notional exposure of $1000 times the index.
VIX futures are available in contract dates out to September. A January contract requires $8800 margin and is sized at about $25,000. A September contract requires $3300 margin and is sized at about $20,000.
The longer dated contracts allow for targeting a date and then having reduced volatility in the near term. That point concerns volatility on the volatility of course.
If the market volatility were to freeze in place for six-months. A July VIX future would rise in price from 21 to the current contract price of about 25. In other words it is expensive to take a sell-side position on the longer dated contracts.
TVIX and UVXY are leveraged ETFs. You can go long or short and on margin as well.