Bert My Old Friend,
I have to say I FEEL your pain and I totally agree that you need some serious time off now and again. How far away is the Next Ped in the Next Town or Two away? There has to be some wiggle room in the rules and laws for a doc who is the ONLY doc in his immediate area to not give Perfect 24/7 coverage.
Personally here's my suggestion. Let's assume that there is at least another ped within less than an hour 50 miles away or so. Hook up as long as they're not a complete Loon and take your own call nearly all the time over the phone via your service that last I knew you still used to handle the initial screen and reach you.
If you can't half handle it at least for the night over the phone then it's probably close to being a Better Safe Than Sorry, I'm Sending You to the ER JIC, Just in Case... Right? And they can always attempt to get in with your new "Call Partner, take phone care with you or for those few exceptions that the patient might be "that sick" it's Sorry But Uncle Bert needs a few days rest too, you're going to the ER. It's one of the few downsides to being in your kind of one of kind solo practice.
But when I talk to you and read about how many years it's been since you've been off, honestly I've been more than just a little concerned for you for a good long time now.
Lastly, the wonderful sharp and such a good egg Lady Ped here in my area that has taught Peds to nearly ever doc who trained here in the past 20 plus years, she finally went solo too about a dozen years ago and couldn't or wouldn't create a cross coverage with the less than personal, less than perfect larger groups in our area. BUT, Dr. P has a good, floating Nurse Practitioner who covers her practice in person when she needs to go overseas to visit family or take a little bit of needed and WELL DESERVED RnR, Rest and Relaxation.
Please Buddy take good care of Bert. You can't properly care for those in your care if nobody cares about Bert and gives him some of this needed time off. Please try to work something like this out... Hang in there and we're pulling for ya....
Paul