I’m really leaning towards your suggestion that oil pressure is low. I will check with the dealer also, but do you know if there is a heavier alternative to the 5w40 oil normally recommended?
I wouldn't mess with the oil weight. 5W-40 is reasonably heavy at operating temperature as it is, going to 10W-50 isn't really going to help.
If you are overcoming an oil pressure problem with thicker oil that will likely be a very temporary fix. If the oil pumping system is so worn, or the oil galleries so clogged it needs thicker oil to get sufficient oil pressure, something is wearing it out like bearing material present in the oil. Even if it raises the pressure it might not increase the flow rate where it's critically needed elsewhere from the transmission.
The oil pumping system for a Spyder is quite complex as it's a dry sump engine, so anything's possible.
In order to get a baseline I would get an oil change, to ensure the oil is the correct weight. I would change the engine oil filter too, to ensure all the gaskets and O-rings are in the correct place and a new filter is fitted and operating correctly. I would also change the HCM Hydraulic Control Module filter to ensure the transmission solenoids are able to release oil at the correct pressure required. For this I would use official XPS branded products, just to know you are good to go on the filters.
This is the cheapest way of knowing your oiling system should be operating properly. When doing this, look for sparkly bits in the oil, to suggest the pumps are worn, likewise sparkly bits in the old filter, and the HCM filter might be clogged.
Unless you have a complete service history for the bike you may have no idea about prior oil change intervals, oil choices, whether it had ever been run low or overfilled, whether anyone had used silicon as a gasket sealant that is clogging things up. Is the inside of the engine clean or is it full of oil sludge and carbon residue? The only way to know that for sure it to at least pull the valve cover off and inspect the top of the cylinder head where the camshafts live. If it is full of sludge up, this is where it will show up for sure. This is not going to be as cheap a thing to do as a complete Oil, Filter and HCM Filter change to get a baseline of things you know.