That's interesting Steve, what is not clear is the signature authority on any sub account or joint account, I suspect you have the ability to make withdrawls alone, if it requires both, the money could be hard to get to.
While it's interesting, I wouldn't go there. Accounts can be frozen and siezed under several events effecting your tenant and done so without your consent or knowledge. Read your sub account agreements with the bank carefully, the right of set off, a judgment being collected may have the ability flow to the master account. Co-mingling funds in a bank account can be a problem as the master account holder has the ultimate liability.
It may be that the op is exempt from escrow requirements if the property is personally held and on a cash basis, you'll be reconizing deposits as income deposited in your general account.
If the property is in a business, you will likely be required to have an escrow account. You do not need seperate bank accounts, just one bank account designated as escrow. Interest might not be paid by your bank on any escrow account, if interest is paid the party due the interest may be dictated by state law, however, it can usually be agreed to, I always received the interest for the maintenance of the account. The seperate escrow accounts for each tenant on on your books, an account for each tenant.
To keep the IRS from attaching deposits as income you need to have a seperate escrow account and agreement limiting your access to funds only upon certain occurrances and showing such funds as a liability. State law governs the acceptance, use and management of escrow accounts, keeping the escrow away from being rents the lease agreement may reference the escrow as a performance guarantee/escrow agreement. Such funds then only become available upon future occurances and while you may have custody, you don't have control.
An accrual system would be a real pain, IMO, for a landlord and as Charles suggested a cash basis would be better.
An escrow account should be cleraly identified on your books and care taken to ensure no accounting entries are made with any sub accounts other than deposits and disbursements applied to each tenant, it's not your money. Some accounting errors could constitute the co-mingling of funds for a business entity. It's always a liability until an indemnification (loss is covered) with amounts assigned to your income or appropriate accounts. For example, if a tenant is required to keep a renter's policy, amounts might be used for premiums and the disbursement made directly to the insurance company, not you, avoiding the income issues. You would then make a demand for the escrow account to be brought current by that tenant, all being covered in your escrow agreement.
If interest is paid on any escrow account and it becomes your income:
Small amounts that do not exceed the cost of maintenance and bank fees, if any, may be allowed to be kept in the account. As interest exceeds the accounts expenses, it become income to you. That needs to be withdrawn immediately as allowing interest to accumulate in an escrow account is basically allowing your buisness income being kept in the escrow account, poisining the fruit co-mingling your money with escrowed funds. Several years ago, this was a big issue with the department of finance in Mo and generated alot of revenues from fines. So, don't ignore your escrow account!
Besides your escrow account, one checking account should do you just fine, move money as you like from that account.
A small business credit card comes in handy at the gas pump! American Express seems to issue more cards, but what ever you get, keep life simple and never use it for personal use, your statements are good source documents for you accountant and the tax man. :)