Maybe I found a solution for my ExpressCards (JMicron chipset jmb363) that was not working after I installed Mavericks.
I have the same MAC than you PO_OLD_MAN and I tried many things for days, testing, booting and doing some tricks. After a week I manage to back my eSata ExpressCard work properly again. Just my GMYLE USB 3.0 doesn´t work properly. It mount but when I try to copy in and copy some files Finder returns a Error Code -36 (cannot write or read from the disk).
So, I did the following:
1)Install (using the Multibeast software) the drivers 3rd Party esata, 3rd Party sata and USB 3.0 Universal.
2)Reboot the system
3)Go to your Mavericks /System/Lybrary/Extensions and delete the kext IOPCIFamily.kext
4)From a installed system of Mountain Lion go to the same folder /System/Lybrary/Extensions and copy the same file (IOPCIFamily.kext) to a pen drive or other place.
5) Back in Mavericks, download the Kext Wizard software and run it.
6) Go to the tab instalation and drag the kext copied form Mountain Lion inside the white box in the window software.
7) Install the kext.
8) Go to the Maintenance tab and select System/Library/Extension (Repair Permitions and Rebuild Cache) and Execute.
9) Reboot the system and conect the eSata HDD.
You´ll have your esata working again.
(I didn´t test everything yet but at least is mounted in Mavericks and I have my esata working again.
Hope that don´t cause other problems.)