65 mph will put a big smile on my face. I have put a short exhaust. A 30 mm carb, 20 tooth sprocket and a more open air filter (undetermined yet) are next on the list.
In theroy: The Electra can go to 65 mph easily, just not recommended for cruising at the speed because of the added stress on the engine. However, with a larger gear ratio, same (not more) speed can be achieved with less stress on the engine. Thats why they have these larger sprockets to begin with.
This theory you stated is not correct.
That theory comes under the heading of "no free lunch".
A larger sprocket actually reduces the torque-multiplier, and places more load on the engine at all speeds. The result is more load on the clutch when starting off from a stop, slower acceleration, and wider throttle openings at all road speeds to increase the engine output to make up for the reduction in torque multiplier of the gearing.
Top speed will not be higher, and may likely even be lower because of "over-gearing".
The "cruising rpm" may be a few hundred rpm lower, but the load on the engine is as high, or higher, than with the smaller sprocket, due to loss of torque multiplier in the gear train.
What you have stated here is a very common misconception. I don't fault you for it. Most people don't understand it. It stems from a lack of understanding of the load dynamics involved. Hopefully, you grasped some of what I wrote above.
However, the Electra can cruise at 65mph, but that's about its limit for long term cruising.
It already comes with an 18T sprocket, which is plenty.
It can do what you want, just barely. The larger sprocket isn't going to be "easier on the engine" despite the common misunderstanding about it.
They make larger sprockets for modified engines with higher output levels to reach higher speeds. They are commonly used for the purpose you specify, but they do not do what people commonly think they do. They trade off a slightly lower rpm for a slightly larger throttle opening. It still takes the same hp to ride at that speed. The result is that the engine is not under any less load, must put out at least the same output, and it isn't any easier on the engine. The slightly less friction losses from the slightly lower rpms is offset by the higher heat output from the larger throttle opening.
It might be a litte easier on the rider, because it's less buzzy at a little lower rpm.
But the engine and the rider are two entirely different things.
The best way to increase cruising speed, or reduce the stress on the engine at the cruising speeds is to reduce the load the bike must overcome to maintain that speed.
And that is done by improving aerodynamics, to reduce wind drag, which is the largest factor of load that the engine must use its power to overcome at those kinds of road speeds.
If you do that, then you truly do have less load, and can then use a taller gear without increasing the stress of the engine, because there's less load to overcome, and the bike can accomplish that at a lower engine rpm more easily, thus you don't need to increase the throttle opening any bigger, and you can use that taller gear to get lower rpms at the same throttle opening as before or maybe even less, because you've cut the load by improving your aerodynamics.
If you want the math, here it is.
(Torque x rpm)/5252 = horsepower.
Lower your rpm, less hp.
.
It takes a certain amount of hp to overcome the resistance loads at speed.
If you lower rpm, you lower hp.
How do you increase the hp back to overcome the load to do that speed?
Increase torque by opening the throttle more.
That's the answer.