The reason Castlefield crops up as a discussion point is because the solutions are hugely expensive, but it is without doubt the biggest single bottleneck and service restriction on rail services not only in Manchester, but further afield.
In a situation like this I would always look at the least cost, quick to deliver solutions first.
So a simple one in top spot, controversial, possibly, close Deansgate station and make alternative arrangements for tram link passengers connections. Its too close to Manchester Oxford Road station, and trains stopping there, particularly eastbound services cause following trains to block the junctions to the west.
Sending more trains into Manchester Victoria then introduces the issue of connectivity between Pic and Vic, which is a serious impediment, a 10-15 minute connection from 13-14 at Pic to the main station turns into a 30-40 minute connection between the two stations. Its also an issue if you have impaired mobility or luggage. But a simple win would be to include tram transfer with all tickets that involve a Pic-Vic change
As well as Castlefield the throat of Manchester Piccadilly is another bottleneck
So another possibly controversial one, No TPE North or South to cross the throat and head down Castlefield or to the airport. There is room to build two more platforms fairly easily to the NE of platform 1 and the scale of works look to be fairly simple. This then gives more room for terminating TPE services, The Airport service then becomes a dedicated shuttle from, ideally, dedicated platforms, maybe alternating fast and stopping services. That removes a couple more services from Castlefield. Costs for this should be realistic. Also make Man Pic 'set down only' on long distance services to the Airport from the North and West, if local commuters twig it, fine, but but dont show them on departure boards. This would help to ease overcrowding on 13/14.
Once you have done the easy stuff you are then into either major surface redevelopment or an underground tunnel, both of which feel completely out of reach at the moment. However if you are spending money I would try and improve Pic capacity rather than sending more services to Vic. The underground option sounds good, but I believe there are various non rail tunnels under Pic and the surrounding area, so may not be easy.