Carefully clean out the high speed jet at the bottom front of the carb. Leave the jet in place, and use a piece of heavy mono -- finish with carb spray using the plastic nozzle.
Work a piece of weed whacker line into the tell tale to try to clear it. Main issue, though, is overheating (160F or more at the top of the cylinder head). Has it overheated?
You can try to clear a blockage in the water passages by pulling the lower unit and pushing hose water up the tube --...
Check and monitor operating temp. Look for 130-140F at the top of the head. 160 is overheating. May be due for a new impeller.
New fuel filter may be restricting flow. Try operating without the filter.
HS jets under screw plugs at bottom front of carb bowls. Don't take out the jets, at least initially. Run a piece of sturdy monofilament through them, followed by a shot of carb spray. Test run.
A throttle cable is typically longer because it reaches around to the port side of the motor, unlike the shift cable attaches to starboard. I'll guess that if one is slightly long for a particular application, there is no harm done.
Rebuild the ignition, then you know what you have: coils, points, condensers and wires. Wires are 7mm with a wire core. OEM if you can, but otherwise Sierra or Mallory will work. Might try a NAPA store to buy everything.
I would opt for a couple of those NAPA batteries, fully checked out. Charge them overnight with your A/C charger when the boat is in the yard. Use one for starting only.
Mennonite families here use lawn mower batteries and solar chargers for operating the running lights on their buggies and shays. They routinely use state and county roads. For your outboard use, I would opt for a pair of regular batteries, using one for starting only. Charge with your A/C...