Keep in mind, though, that a higher offer is not always considered the most desirable. I can give you plenty of examples of sellers accepting slightly lower offers that are much more solid, rather than accepting a slightly higher offer that's much less certain. A lot of people who would be buying with an FHA loan are finding that their offers are being rejected in favor of people who can put 20% down. And the 20% down folks are sometimes losing out to people who are putting in all-cash offers. There are also a lot of contingencies that can weaken an offer--for example, if you were a seller which would you take: $350,000 all cash, or $375,000 contingent on the sale of a current home? Or if your home needed some repairs, which would you take: $350,000 in as-is condition, or $375,000 contingent not only on a home inspection but on the repairs being made?
As a practical matter, there probably are other ways the seller could get out of the current agreement if he/she really, really wanted to. But unless there's something highly attractive about your offer, the old saying about "A bird in the hand is worth two in the bush" applies.
As others have said (and I said in my previous post to your previous question), the highest amount of money does not always win the contract. It is a total package of financing, terms, contingencies, and timing.
Best wishes to you.
You want to go ahead and make sure your financing is as ready as it can be - try to shorten that 21 days. Ask for permission to have your bank appraiser go before you are in 1st position. (Ask sellers agent, and double check with your lender that lender will allow this). Sure, you will pay for an appraisal you might not actually be able to use, but it sure would make your offer more compelling to the seller, don't you agree?
Also, have you done your home inspection yet? If not, consider spending that money now, and doing it, and waiving that contingency too.
The bottom line is the bottom line, is it not? Spending a little now to improve your offer might be the reason you get the house.
If you're only medium-hot on gaining this property your strategy might not be so proactive. Maybe instead of doing both the appraisal and inspection costs, you just do the inspection cost now.
Talk with your agent, and see what his/her advice to you is.