I haven't tried the HMEC 26 personally, but have heard good things about it. All I can say that the very different HMEC 46 is crap, bad noise cancellation and ears get sore very quickly.
I have tried Telex 750 (terrible), Telex 850 (not good), Sennheizer HMEC 46 (not good see above), Clarity Aloft (very light, quite good but it's not for everyone to use a in-ear headset), Bose A20 (best noise cancellation, but high clamp pressure), Bose QC-15/Uflymike (very good), David Clark Pro-X (very good)
I can recommend the Bose QC-15/Uflymike combo. Good noise cancellation, very light and takes half the space of a A20 in your flightbag. Not officially approved no, unless you send to Uflymike to make it TSO approved but a looooot of pilots are using this. Uses 1 AAA battery and lasts about 35-50 hours. Will start blinking 4-5 hours before going dead, downside is that it goes completely dead when the battery dies. But you will notice well in advance. The whole combo costs around $500. And also I recommend the David Clark Pro-X. Good noise cancellation, rather light.
Personally I find the A20 to have way too much clamp pressure (at least for my head shape, yours might be different), quite heavy, takes a lot of space in the flightkit, but undoubtably has the best noise cancellation there is.
Cannot say how the RYR aircrafts are except that they are very much "harlem" versions of the aircraft (1 HF and no SELCAL????). But I know of incidents where some headsets have fried the aircraft's audio box (738) in the ones that do provide power to the headsets. Many newer 738's have the XLR-5 connector (after 2006 I think, but could be just an option)
Personally I have a headset with XLR-5 and an adapter for 2 jacks for those aircrafts. Again I do not know which ones the RYR's have.
My advice to you, don't save money when buying a good headset. A career ahead of you in a noisy 738 flightdeck, I would get a good headset with good noise cancellation. Even though you might have to pay big bucks for it, it will still be worth it. Over time your hearing will degrade with a bad headset, and that cannot be fixed. All you can do, buy a good headset.