Re-fixing b&w film negatives

I'm a first time developer, and I've been using Bergger Monobath to develop some ooooold rolls of 120. The first five rolls came out fine, but the last two appeared milky along the edges after drying. My understanding is that this is a fixing issue, and that likely the fixer in the Monobath is no longer sufficient to properly clear away the silver halides in more demanding conditions (old film stock, along the edges). For this reason, I went ahead and bought some separate fixer, intending to just run the negatives through some fixer and see if they improve.

I'm having a hard time finding a description of this process, wondering if I should 1. Wet the film first as if I were starting from step 1 and 2. If I should follow the same time / process / agitation schedule that I would if I were doing the whole process or if I should shorten the step since it already fixed to some extent.

My instincts say yes, wet it first, and yes just do it for the normal amount of time because it's unlikely I will over-fix in that time period. But I'm new to this, so want to double check.

Thanks in advance for any help.