I thought most MD recorders could provide decent plug-in power. maybe another reason to think about upgrading mics instead of box
NO! The MZ-RH1 is a truly great recorder, but the plug in power voltage is low (possibly as low as 1.5 volts). You need a battery box or preamp to record reliably.
The MZ-RH1 has a great preamp on board, so you could go with a small battery box, like the one from Chris Church ($30). I love his ST-9100 preamp for it's versatility, but you might not want to spend that much.
You should be able to make great sound recordings with your mic and a battery box, but it only handles SPL's up to 120 dB with a battery box, so you could occasionally run into distortion if you were trying to record an ear crushingly loud concert too near the stacks.
When you have the cash I would add something like the CA-14 Cardioid to your arsenal. It will handle higher SPL's and there are times a cardioid is better than omni or binaural mics (such as when you are far from the source, the room has bad acoustics, or you want to reduce crowd chatter behind you).
Tips on using the RH1:
I generally go line in, but mic in works great too with or without the -20 dB switch on as appropriate (for loud music you would always want it on).
Do not use auto level control. Set levels so the meters peak in the -12 to -6 dB range so you have plenty of headroom to avoid clipping. You can use the Hi-SP mode if you need more than 93 minutes recording time without swapping discs. I hear no audible difference between that and PMC mode. Make a test for yourself and see if you can hear a difference (you're younger than me).
If you are going mic in and and you have to set your levels below 12 to keep the meters from going over 0 dB, you are likely to get a brick walled recording that will sound terrible. Instead of going below 12 switch the mic to the line in input where hopefully the meters will stay below 0 dB with the level set at 12 or higher.
For low profile recording keep the RH1 in your shirt pocket so that you can monitor the levels just by looking down in the pocket. Cut a hole in the shirt pocket for the cords and run the cords out your shirt collar behind your neck. You can easily fit an RH1 + a battery box or ST-9100 in a shirt pocket.