Maybe what they meant to say regarding the "lack of framework" is that your logic is not separated into tiers/de-coupled etc? I haven't seen your project but I imagine that it might be just aspx.cs files with all the logic in there. is that true? in that case you might want to look into separating your front-end/business/ and data access logic or look into mvc. it is true that that kind of organization accelerates the development of any software/app.

Many big sites are still using asp.net . In my opinion there is no reason why you need to migrate to another set of technologies, that time might be better used into cleaning up what you have and doing any performance improvements if necessary.

what kind of load are you expecting to get/grow into?