If you don't want the bulk of a scope mounted on your rifle then a peep is very accurate. I have a Williams peep on my Win 94 and my Marlin 1895 and I find them easy to use and very accurate. I also recently installed a tang peep on my Hawken but have yet to try it because of mechanical issues with my lock.
As for your fiber optic sight issue, the Williams Fire Sights are the same fiber optics (GM puts them on their ML barrels). Most of us older guys have trouble with the front sight blurring out. I've found a little trick to stop that and that is to put a light coat of white out or white fingernail polish on the side closest to you. Only a light coat though. This reduces the glare but enough light is emitted through it to be bright in low light.