A Center Controller reported an Air Carrier was left on a heading too long and flew below the Minimum IFR Altitude.

Narrative

I took over sector ZZZ (mid configuration). Aircraft X was on a vector for the localizer at ZZZ in sector XX. There was higher than normal ZZZ arrival traffic in sector XY. In mid configuration we are operating with this combined sector on a 180-210 mile range. Aircraft X was on a heading that took him through a 11000 ft. area east of the ILS. I was trying to split my attention between him and numerous potential conflicts between arrival and departure traffic in sector XY; which is also difficult to work at over twice the normal range. I turned Aircraft X back prematurely and he came in high on the localizer and did a 360 with tower to lose altitude. Combine XX at XH:00 prior to the mid shift coming in so that XY and XX can be worked at closer to a normal range. Staff for people on the XA00 to XI00 shift so that we aren't pressured to combine sectors early to get people out to go home. Rearrange sectors so that we don't have to do a logical to physical swap prior to the mid shift; which puts pressure to combine XX/XY/XZ before it is advisable to do so.