Accrual methods make sense when you don't have a physical product and invoice at regular intervals, especially if you have any type of retroactive invoicing and/or charge any type of interest or are remitting to a third party.
Cash methods would be nightmarish in this circumstance.
This pretty much exactly describes a huge portion of the business we do. I've found cash basis very very nice in comparison to accrual for this exact use case. (And was what was recommended by an accountant in particular).
Does your accounting software make it unable to track invoices if you're not doing accrual or something? Mine does invoicing, AR, and other accounts just fine.
Cash methods would be nightmarish in this circumstance.