There's a new MSP-ICN flight operated by DL that's been announced. Have you checked whether it will operate when you need to travel? Otherwise, if you want to avoid KE TPAC flights to ICN, the obvious choices are to connect through hubs where DL has a nonstop to ICN, such as DTW, ATL, or IIRC SEA. You might also be able to take the MSP-HND nonstop and then do Tokyo-hub/hub-ICN on a suitable SkyTeam member, but doing this will waste a lot of time.

Once you're in ICN, the SkyTeam operated flights to PER that don't include at least one KE or Chinese partner are much more limited, but you might have more choices if you call DL to book (versus what's on delta.dumb) or use a real live human travel agent who can construct itineraries segment by segment, assuming that the carriers interline.

Note that the Virgins aren't SkyTeam members, just DL (and AF/KLM bilateral partners), so your choices will be very limited. Try looking at schedules for desirable (not KE and not a Chinese carrier) SkyTeam members that fly from ICN to somewhere in Asia and simultaneously such partners that serve PER.