I would not mangle the block by cutting a hole to use a camera.
Reasons why.
Those engines part out really good. (you currently most likely have a good block.
You will not be able see and really inspect good even with a good camera.
Those engines with the oil pump are user friendly to take apart for someone like you that has patience. (patience is one of the main things when doing anything)
Do it in your spare time eventually.
Labor costs of shops for such has it's limits.
No special tools are required to take the sump off and inspect the camshaft. (or to put it back together)
Lots of you tube videos about how to remove the sump and re-install on that engine and inspect the camshaft, remove cam, re-install, etc. Do remove the carb and intake as it can be easily broken. You can leave the flywheel on the engine to remove the sump cover.
I've used the china clone gasket kits instead of the pricy Briggs real deal stuff on that model Briggs and they work good.
You might get by without pulling the head, just loosen the rocker arms.
One of the first things to check for taking apart is use a really good 5/16 6 point socket on the 3 oil pump screws and do not round off their heads. Some are really tight and have tendency to want to not come out and if the socket slips it will round off their heads and then require additional steps.
A big metal bread pan or a big plastic lid is good up on a piece of plywood on sawhorse is good for shade tree. the pan catches/captures any oil dribbing and any small piece that might try to escape.
One thing that I would do before taking it apart is run a leak down test. (or even ask a small engine shop their labor cost for doing such)
You can probably rent such from a Auto parts store
Only takes few minutes when experienced and is one of the first things a good small engine shop should do instead of just taking it apart.. You can review such on-line for a single cylinder small engine.
Also good Briggs experience if you want to become more independent of repairing your own mowers.
Also don;t be surprised if the engine mounting bolts twidt off. Sometimes on old Aluminum block Briggs engines the 9/16 head steel bolts are gall seized in the aluminum block and one or two might twist off. Best to not start the removal process with a impact wrench and use a good 6 point socket. Start manual removal with 1/2 inch drive breakover or long handle ratchet.
If the engine mounting bolts twist off or the head rounds off you are immediately SOL.
