Us older guys up here in eastern Canada always figured 5w-40 is too thin an oil for these old diesels in any season. Certainly in your areas summer temperatures.

There are a lot of actually minor things to check for hard starting in the winter. I do not want to start an oil thread either.

There is also a chance your new oil de varnished the old lifters a little. Running a 15-40 synthetic oil in the winter and summer is probably okay. 5w-40 may be asking for real trouble.