So apparently, ingemuit is the perfect form of both ingemere and ingemiscere.
Virgil never uses the present of the inceptive, but does use the present of the former one time:
Extemplo Aeneae solvuntur frigore membra:
ingemit, et duplicis tendens ad sidera palmas
talia voce refert (1.92-3)
He uses the perfect form six times:
num fletu ingemuit nostro? num lumina flexit? (4.369, Dido talking to herself with Aeneas present)
ter sese attollens cubitoque adnixa levavit,
ter revoluta toro est oculisque errantibus alto
quaesivit caelo lucem ingemuitque reperta. (4.690-2, Dido dying)
Dardanidae, quos ille omnis longo ordine cernens
ingemuit (6.482-3, Aeneas seeing Trojans in the underworld)
ingemuit cari graviter genitoris amore,
ut vidit, Lausus, lacrimaeque per ora volutae (10.789-90, Lausus witnessing Aeneas attack his father, Mezentius)
At vero ut vultum vidit morientis et ora,
ora modis Anchisiades pallentia miris,
ingemuit miserans graviter dextramque tetendit,
et mentem patriae subiit pietatis imago. (10.821-4, Aeneas after fatally wounding Lausus)
utque procul medio iuvenum in clamore furentum
prospexit tristi mulcatam morte Camillam,
ingemuitque deditque has imo pectore voces: (11.838-40, Opis mourning Camilla's death, and about to take vengeance on Arruns)
So I was wondering if there was any point in trying to distinguish the two. Or is there really any difference to distinguish, in English at least? Maybe just 'combining' the two for "began to groan out/over".