I think it's just possible that 'at' has been mistakenly taken to mean 'in the place of' (from the Chambers entry - 'for') rather than 'instead of'.
Also, I think STOWED would fit the definition at 28d in the sense of 'swallowed' rather than 'intoxicated' (Chambers entry - 'stow') 'to put down one's throat (joc.)'.
The wordplay is weaker - because SLO(g) is better than STO(t) for 'tramp' - but, like others, I can't find a dictionary entry giving 'slowed' for 'drunk'.