Well, I thought you didn't want the expense of using matching frames, skirtings and architraves in hardwood? I think you either decide to match the oak with solid oak or else you go for painted softwood, there is really no benefit in trying to use a cheaper hardwood for the frames etc (not that there's likely to be any saving in using ash, meranti etc in place of oak). I've seen oak doors with painted frames, skirtings etc and it looks well, it's certainly a good option if budget is a concern.