I've stored many Amigas, retro computers, old SCSI hard drives and other hardware out in my garage here in Canada (-30 to +5 C) during the winter. Some have been out there for years and I've never had a hardware problem with any of them.
The fact that your Amiga behaves WORSE when first starting, and starts to behave better after having been on a while, would seem to indicate to me dried out capactors (i.e. slow to hold a charge). I know you've had them all replaced, but perhaps one was missed or a bad/old capactor was used in the replacement?
I think a good start would be to replace ALL capactors that have not yet been replaced.
