I could see the following potential causes (except your safelight which you say is proven innocent):(posted 9194 days ago)1) Recently, I read that the fumes of sepia toner may fog papers. I am sure that other physical (heat!) and chemical influences can achieve the same. To exclude this, process an unexposed sheet, preferably in total darkness, and check whether it is base white after processing. For comparison, fix an undeveloped sheet to exclude the developer as the source.
2) Stray light reflected from any gleaming or white object near the path of light from the lens to the easel. Check the enlarger column, a white wall nearby, ...
3) A light leak somewhere around the negative carrier of your enlarger or reflection of light from the top of enlarger from the ceiling.
4) Lit scales of any instruments (timers etc.).
5) As one other post states, the highlight are determined by exposure (as are the shadows in the negative). So you could choose a shorte exposure time and use harder paper to get the shadows right. This will not give you a fine print, but it should work unless the negative were really severely underdeveloped.