In answer to your headline question the answer depends on the terms of your contract of hire. If you agreed to pay for results - then I would say you owe nothing, if he/she finds nothing. This is similar to the "no win no fee" deals advertised by some lawyers (although even then you should always check how you stand on their expenses as lunches, photocopies, secretary, stationery, filings etc can soon mount up).
If however you agreed to pay for his/her time, expertise, reasonable expenses and experience (as is more usual) then if nothing is found then you still have to pay - but at least then you have some level of reassurance that there is nothing to find and you would not unreasonably expect some narrative or listing of what sources he did check so as if you do ever decide to delve even further then at least you know for sure what has been already checked.
I cannot see that "standard research" is going to unearth much at all. Sounds to me that you have already gone a long way with your researches and investigated sources well past the remit of standard research.
However maybe you could change the focus of your questions a little if you want to plug on - maybe you could try looking into and asking around as to why so few records are available....you said you had found a few, so why were there not more. In a similar vein maybe you could ask if people you have asked already have heard similar enquiries from others and if so, who knows maybe you could be put in touch to at least compare notes or even verify each others findings.
Personally I enjoy ancestry research a lot but I cant imagine spending thousands of dollars on it. If I had that sort of money to spend on genealogy I'd rather take some time out, prepare my stuff including asking others what I could possibly look up for them, and go on a tour of cheap motels looking at old family haunts, churchyards, museums and records repositories by day and enjoying the nightlife later, but that's just me.
If I was minded to spend a couple of grand on this particular genealogical problem I wonder if trying to do it by looking endlessly for records that many very well not exist is the way to go. Maybe the money would be better put into doing some DNA testing and expert advice on that. The Peoria tribe are a relatively small grouping and so you may well be able to find out (assuming they are cooperative) which bloodlines in the village you are closest to and thus find living relatives of some degree even if the far ancestors remains somewhat clouded. This is particularly possible as I understand that male DNA is much easier to trace with certainty than female DNA (as the Y chromosome is only in males and mutates very slowly). another good thing about DNA research is that once it's done all the time new people are being tested, so unlike a records search where drawing a blank now, means it will be a blank in 10 years time too (unless some new records are found and added) with DNA there is always a chance some close match might come along at any time in the future (and without any additional work needed by you). It strikes me DNA research would certainly be a more interesting, informative, refreshing and scientific way forward rather than spending on what is likely to be paying out to learn little or nothing on a records based search.