ARTCC Controller reported a situation where they canceled an aircraft's approach clearance and issued a delay vector and climb; the aircraft was slow climbing to the assigned altitude resulting in flight towards terrain.

Narrative

Aircraft X was requesting a VOR-A approach to 3U3 with an initial at CPN. I had another aircraft that I was attempting to get into BTM on an ILS approach. The missed approach on the BTM ILS climbs out over CPN. The BTM aircraft had reported below 090 and I cleared Aircraft X to cross CPN AOA (At Or Above) 100 for the VOR-A; planning on them being clear of CPN before the BTM aircraft reached the MAP. By this point the BTM arrival was below radar coverage. I asked Aircraft X to verify that they were planning a straight in from CPN. They said they were planning a procedure turn. I attempted to cancel their approach clearance and give them a delay vector with a climb to back to 110. They did not initiate the climb until they were already in the turn and got into the 109 box south of CPN before they reached 110. Recommendation:Verify straight in or PT (Procedure Turn) further outTurn the aircraft further to the north and verify climbing prior to the turnHold one aircraft until the other has completed the procedureImprove radar coverage in the BTM-3U3 areaModernize 3U3 approach to deconflict with BTM if possible