Mobile marine mechanic here. Good advice above. Before you talk about a repower, split it into two problems and test each one cheap.
Shifting:
1. Disconnect the shift cable at the engine and move the shift arm by hand. If it clicks into forward, neutral and reverse with light effort, the engine side is fine and the problem is the cable or the control box.
2. With the cable off, work the control handle. Stiff or gritty means the cable is binding (corrosion inside the jacket) or the control box needs service. A stiff cable also gives you the "can't find neutral" problem because it won't push the shift arm all the way back.
3. If the engine side is stiff with the cable off, then you're into the shift rod and lower unit, which is the bigger job.
Spongy RPM:
4. Check the prop hub first. Mark the prop and the hub with a paint pen, run it hard, see if the marks moved. A spun hub gives exactly that rev-up-with-no-pull feel after a long troll.
5. If the hub is good, do what seasick said: fuel pressure gauge on the rail, then the primary filter under the cowl and the VST screen. A long troll followed by a hard pull is the classic way to expose a fuel supply problem.
Both checks are a few hours and cheap parts before anyone pulls a powerhead.
General info only. Always follow your manufacturer's service manual.