Sounds like a good plan.
But, I think you can extend your riding season, by buying some nice merino wool tops and a pair of tights and/or leg warmers. A lightweight merino top with a base layer doesn't have to be cycling specific, you can wear it under your jacket, and can wear it for walking, hiking, whatever. Look on discount web sites. Arm warmers, leg warmers, and skull caps are relatively cheap, in terms of cycling clothes. Spend the $ on a good pair or pairs of gloves. Before I accumulated a whole bunch of different levels of long fingered gloves, I used the Terry light weight long fingered gloves, and wore thin merino liners under them, or silk liners.
There's a lot of riding to be done in April and May, as well as October and November. You don't have to ride in the rain or bad weather, just cooler temperatures.
2015 Trek Silque SSL
Specialized Oura
2011 Guru Praemio
Specialized Oura
2017 Specialized Ariel Sport