A GA aircraft has exactly the same amount of priority as a B747.
However a GA aircraft causes a very high degree of workload as they are so slow.
In your CPT senario, all jets westbound from LL have to be climbed through your level, everyone will be on headings or these jets will be asked to expedite climbs to achieve the required separation.
I have not mentioned the northbounds from HI or deps from GW etc.
I think you were after some advise as well, so I think it would be better to avoid the main westbound flow to the USA, from about 1030 to 1300 local.
In the distant future, it would not surprise me at all if your type of flight was banned, due to the increase in CO2 emmissions and fuel burn it causes to other aircraft.