There are a lot of unknowns here so that's probably why none of the other volunteers have responded, I'll do the best I can to help.
You'd written "very wide"...that's a relative term, is that 10s, hundreds, thousands of columns? Personally I find that I start having problems in Prep when the row count gets into the hundreds and I've got multiple steps involved.
Also you haven't said anything about your hardware (particularly RAM and available disk), that can also have a big impact.
At this time Prep attempts to turn the flow into as few queries as possible that can run on the internal Hyper DB. Given the combination of Hyper & Prep's current (as of 2020.1.4) capabilities this can cause Prep to create massive queries that consume large amounts of memory and make flows really slow (or throw query too large errors or just plain fail). This is in contrast to other tools that can process in a more step-wise fashion and consume smaller amounts of resources at each step (and therefore run faster). This points at the present workaround for Prep, which is to break down the Prep flow into a series of smaller flows. This is more complicated to run, but it's a known workaround.
If you can I'd also suggest submitting a support ticket to help give the Prep developers more information about where Prep is having performance issues.