I just went through the experience of shopping for a flashlight that meets my needs and you have similar requirements. I found that modifying my Mini Maglite® was the way for me. I used Dat2Zip's 500mA NexGen sandwich with the UX1K emitter. It's sold as a drop-in kit on his website.
The sandwich modules will run on alkaline, Lithium or NiMH AA cells. They draw a lot of current, so the lithium or NiMH cells are the preferred powerplant for these modules.
It has made my dim little light into a light that produces more light than my 3-D cell Maglite®, not just a little more, but WAY more. The D-cell light still throws a little better if it's focused to the tightest spot, but the overall light output of the sandwich makes my whole backyard visible, not just the one spot.
My minimag is now the flashlight I wished it was when I bought it. If anything, it's a little too bright for some close-in uses, even when my eyes aren't dark-adapted. The only problem might be runtime, with the latest NiMH cells, they seem to get about 2-3 hours of runtime. AA cells are small enough for me to carry spares, and cheap enough to stockpile.
The problem I kept running into was that I wanted a bright LED flashlight that was about the same size as my minimag that used AA cells. I need a light that is small enough to keep with me all the time. There just aren't a lot of options in that arena. The Streamlight JR Luxeon came close, but for some reason it's longer than the minimag, and rechargeable cells aren't recommended. It's only semi-regulated, rather than the sandwich's constant-current regulation.
I can't recommend the sandwiches strongly enough.
My setup was a bit over your target price. You could go with the TY0J emitter with a 750mA converter board, it's $50 + shipping. Both come with optics, but you may want to upgrade them to the 17mm IMS reflector, from what I have read, it produces a superior beam with good sidespill. The IMS is an extra $2.00.
The TY0J emitter is less efficient than the UX1K and will drain the batteries faster when used on the 750mA NexGen board. I spent the extra $15.00 on the UX1K @500mA, but I don't know if it's as bright as the 750mA TY0J. I suspect the output is pretty similar.
Some other great extras for the minimag are the Kroll tailcap switch and the 22.5mm flat mineral glass. The twist switch was my lease favorite feature of the minimag, and the plastic lens didn't help anything.
Here's the link to the Sandwich Shoppe:
http://theledguy.chainreactionweb.com/index.php/
I'm considering the Fenix L1P as an indoor/backup light, but I only just contracted flashiholism, so I haven't had a chance to play with one yet. I got my mom a River Rock 2xAAA light at Target and it's perfect for indoors, but it runs on AAA cells, making it not very useful to me.
Hope this helps,
Jon