The point you make is a good one. Frequently the method chosen for tax purposes will be a poor choice for internal management reports, as it won't give an accurate picture of the company's true economic performance.
The answer to how to best handle the dual-method accounting is, I'm afraid, "It depends." Generally, go with whatever procedures involve the least amount of work.
In other words, you're looking at either keeping the books primarily on a cash basis and then periodically producing accrual-based management reports from the data, or (vice-versa) keeping the books on the accrual method, and then periodically generating cash-based tax returns from the data.
Which one is less time-consuming will depend on the particulars of your situation. More often than not the latter approach is probably more efficient, assuming the management reports are produced much more frequently than the tax return.
How you'd physically go about it is also fact-dependent. Some accounting software packages have that functionality built-in; they can produce cash-based and accrual-based statements on demand. E.g., as long as the software knows that a sale to a customer occurred on March 22, and the customer paid on Apr 17, the program would include the sale and the receivable on a Mar 31 accrual P&L, exclude it on a Mar 31 cash P&L, and pick it up as an April transaction on a cash Apr 30 P&L.
If the software won't do the heavy lifting for you, it's usually not a difficult thing to do yourself with a few simple adjustments at year-end. For example, just lay your Dec 31 final accrual-based numbers into a spreadsheet. Then, with an adjustments column, zero off the receivables and the corresponding December sales that created such year-end receivables. Do the same thing for the Dec 31 payables and the December expenses that created them. Similarly, have an adjustment column which brings back in to the current year those end-of-last-year adjustments you made; i.e., the payables you paid back in January, and the receivables you collected in January, which should be considered expenses and income of this year under the cash-basis method.