Complaint from 12 who ran with 2 inveighing against 5 leadership (7)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

The ‘Tory who ran’ is [Sebastian] COE; the solution to 2dn, ‘Liberal’, gives you L; and IAC comes from the initial letters of ‘inveighing’, ‘against’ and ‘Corbyn’, which is the solution to 5ac. All a bit convoluted, you might say. I might say that the clue doesn’t work, since you can’t equate COELIAC with ‘complaint’. Coeliac Disease is the illness. You can describe someone as a coeliac. But the complaint isn’t called coeliac. I have two children who are coeliacs, so am more than averagely qualified to make a judgement on usage here.