It is very rare to get a rate lock for longer than 90 days. I do not think that you are being taken advantage of here. You should, however, weigh the additional costs and fees of the rate lock compared to the possibility of lets say (worst case scenario) the rates go up .5% over the next few months. It may be in your better interest to just ride it out and lock in within the typical 30 day window. To me it would be worth the $5,000 towards closing to stay with the lender.
Not sure you are going to find any options for locks longer than 90 days on any government loans (VA, USDA, or FHA). I have never seen them offered at any place I have worked, or sent loans to. HOPEFULLY, we have seen the worst of the recent rate hikes, and as you correctly observe, doing a 60 or 30 day lock would give you better pricing, if the market doesn’t continue to decline in the meantime.