Dead right.
There is a system for striking onto the wrong side of the finger, lifting that finger out of the way of the closing bail-arm and transferring the line; someone posted on here and I'm blessed if I can remember which saint it was!
The smaller Mitchells went the right way round - look out for the 315, 207 and 209 (the latter has better quality gears), 309 and 409.
Abu laid a bit of an egg with their 663,664,665 series, which had the line lay correct for southpaws; they and the simpler Dragmaster DM2, DM3 etc. series often turn up on ebay.
As for centre-pins, its only really the placing of the check lever/button that can be a small annoyance, unless some goon has irreversibly fixed a line-guide on the side you don't want it.
A decent Trudex, with its line guard (which can be removed for calm days and Wallis casting BUT store it and the screws somewhere VERY safe) is hard to beat for the money - about £40-50 on ebay (risky) or £60-80 for a safe one from a known dealer - Jim Hudson at the Vintage Tackle Company springs to mind.