The lamp should fit if it's the same wattage/length. However, lamps in different fixtures have different irradiation patterns (https://tortoiseforum.org/threads/t5-uvi-comparison-arcadia-vs-sun-blaze-fixture.184441/), having a Solarmeter 6.5 for measuring UVI will be very important.
Maybe, @jaizei know what ballast Arcadia uses.
It's not possible to get the ballast out without cutting the wires and having to resplice the wires to reassemble it wasn't something I wanted to do, so I've never fully taken an arcadia light apart to see. But from the ends, it looks like its just OEM and not a 'brand name' ballast you'd recognize.