Not sure if this is a better idea, but it works!
1. Take care of existing customers first.
2. Don't waste time on tire kickers, not even for a trip charge. Explain that you are very busy and that you prefer to look at a job prior to giving price; however, due to your backlog you are willing to make an exception and give a range over the phone. If they are fine with this range, schedule and do the job making the profit you deserve.
3. Efficiency is paramount - schedule jobs by location and severity.
4. Offer discount to customer if they are willing to wait a few days.
5. Find an extra pair of hands for anything that can be delegated (paperwork, telephone calls, picking up materials etc.)
6. MOST IMPORTANT - If they absolutely cannot wait and there is no way you can get to them - refer them to another reputable co. like Smells suggests. Before referring, get their tel. # and address. When you get a chance, send a letter explaining all customers are important and that you were very disappointed that you could not get to them. Ask them to consider you the next time a plumbing need arises and offer them a coupon to do so. We have turned down a total of four jobs in four years due to being too busy. Three out of the four customers came back to us. These are customers we had never worked for, but all stated they were impressed we went the extra mile to hook them up with an excellent plumber. The plumber we refer them to is excellent, but by himself. He refers a lot more to us than vice versa.
Hope this helps a little!
BTW - We are slammed now too and understaffed!