Try a Kai Mild in your Claymore. I really think you will like it based on what you say.
Ok.. I just had a brilliant shave with a Kai Mild in my Claymore Evo... every smooth. It's hard to remember the first shave with the Schick Proline, but I suspect they are similar. I remember thinking I'm going to like this P-30... but then that third shave was a struggle. I'll run the Kai until it dies.They are also prone to having one to two misaligned blades per pack. I still use them, 3 times and that's it. They tug after that in a shavette. The Kai Pink are the same, but they start off smoother and less sharp. They could go 6-8 shaves for people with less difficult beards. I always hate binning them. I told you the blades will behave different in a shavette...
Even though the Feather ProGuards are not necessary in a SE razor, I get 6 comfortable shaves from them.. and the first few are even closer than either the Schick or the Kai.
Yeah, I figure I'll have to redo all the testing in a barber razor...not the same set-up. But I'll get advice here before I start.