Are there any freight flows from Southampton along the coast? Either current or historical?
Currently (or at least fairly recently) there are aggregate flows to Chichester and Botley. I think the Chichester workings do run from the east (from Redhill via either Arun Valley or Hove, not sure) but the Botley runs are mostly arriving from Eastleigh. The only freight on the East Coastway are a couple of flows between Newhaven and London (dredged aggregate and flyash from the incinerator IIRC).
Eastbourne platform 1 could have 12 coaches/ wagons on , and the run around loop is really quite long (alot of sidings in Eastbourne as well, 9 i think)
The headshunt and crossover takes off 4 cars of that (nicely illustrated on Google maps by the unit in the platform!), and the loco attaching on the end would need to fit back behind the signal, so your effective length is 8 cars, minus loco standage so c.140m. There is not the pointwork to arrive directly into the runround road, so you can't have a longer train and run the loco back using P1.
There was an occasion recently where an overlength train was mistakenly sent down the East Coastway bound for Newhaven when the branch was under possession. AIUI it was routed through Hampden Park, stopped short of Eastbourne, and then ranround on the mainline between Hampden Park and Eastbourne (the reversal at Hampden Park is signalled, as is the crossover move from the Down Main to the Up Platform there). However you would not be allowed to plan for that move to happen.