The old series is indeed a mess as far as storytelling is concerned. It should have ended with SotN. Perhaps picking back up with Soma's whole reincarnation thing, but still. Those games were built for gameplay, not story logistics, which is fine. Or was. Now, there is no reason to ignore one for the other.
I'm entirely on board with either Staying with the LoS universe a little while longer or starting from scratch again. The LoS universe still has and will have plenty of stories to tell, though not including Dracula. The Belmonts obviously continued after Simon, so one can presume they continued the legacy of Simon since we get Victor in LoS 2. Richter, Johnathan Morris, etc. could all have their own games, just without having Drac as the big bad. Richter could face off against Shaft, and Morris could aim to stop Brauner, was it?
Potential there, I say.