As you are aware, I am able to run my HM on a CAT5 cable up to about 50ft, being long tested (years) with a many cables.
I am not sure why you are having issues, if you do not see the voltage drop with a short cable but do with a long cable I would suspect the following:
Poor CAT5 jack on either the HM or RD. If the pins are corroded or bent so they do not provide solid connection that could be an issue. Or could be solder issues on the CAT5 jack at the HM.
Poor connection to the punch down knives in the RD CAT5 jack. You can cut away the plastic and solder wires to the knives to assure 100% solid connection there.
Poor quality CAT5 cable or bad crimp/ends.
Weak power supply or issue with the HM power regulator circuit, or bad solder joints on the HM board. If the PS browns out under load, or the Vreg circuit has issues, your HM may buckle under a load. I would check the soldering on the entire vreg circuit, check component values, particularly the capacitors and the polarity of electrolytics.
I make my own cables, have been using old school solid core CAT5e wire and the ends you can get at Home Depot. If you pay for shipping I would be glad to make up a long-ish CAT5 cable and send it to you for free, I have lots of this stuff sitting around. I will test it here with my HM first so we KNOW it works, then we will see what it does with your setup. Just shoot me an email and let me know what length cable you need and I will crimp one up and send it to you.