Hi,
I am in the exact same position as you. I also have and use the XLR breakout cable and the AI4S and AO4S 4-Channel analogue I/O modules.
It seems that every solution I find appears to come with problems ranging from fitment to added noise or electrical interference. I have been looking at a StarTech PEX2PCI4, which is an external 4 port PCI enclosure that connects to a PCIe interface card via an included DVI cable.
It seems that a member of this forum successfully used this method to house an HDSP 9632, HDSP 9652 and an HDSP 9652 Expansion. He seemed to suggest it was working fine. I am fairly sure it was the same person that left the following review for it:-
"The box was detected directly by Windows 10 (x64). A driver for the external PCI-to-PCIe solution is not required. I was able to put the RME audio cards and extensions into operation as usual. Unlike other manufacturers (presumably replica), the PC with the connected original StarTech box starts even when it is turned off. This is even useful in my case, since the external audio hardware should not be active all the time when I use the computer for other purposes. Only when I work with Steinberg Cubase Pro, for example, I switch on the box before starting the PC to access the external audio hardware.
Because the RME audio cards and extensions used in the PCI slots are silent and require no fans, the StarTech PCI Express Expansion Box is an ideal external solution for all users who use current motherboards but don't want to miss out on PCI slots to continue using their audio equipment"
I thought this sounded very promising but, as with any product, I also found a not-so-great review stating the following:-
"If you manage to get your devices working, and these are older cards, which may have once been audiophile quality, you may find that the sound floor has significantly risen due to the pci-e bridge introducing a significantly higher sound floor noise (distortion); this means if you have analog cards being powered by dirty power, that will be introduced into your output signal; in return will then get amplified by your gear; you will hear distortion due to this. The power block used by this device may be replaceable such that you might use a linear power supply to clean up the snr, but do at your own risk. I've already had to replace the entire rig once. I won't do it again. Every time you open this thing up / close it, you risk breaking it, and your cards inside"
Finding a solution is driving me mad too :)