Firstly, I'm sorry that you lost your wonderful companions and I know how difficult that is. The problem is that the Basset is a pretty unique dog in every way. Looks, temperament, character and size.
You could look at the other Basset breeds ; Grand and Petit Basset Griffon Vendeen, Basset Bleu de Gascogne or Fauve de Bretagne. Or would you feel able to look at a larger breed, like the Bloodhound? Personally, I think the breed you are familiar with will be a hard act act to follow, especially as you've had six of them. I'd probably be inclined to stick with the hound group at least.
We were in the same situation when we lost our 7th Pyrenean six years ago. We couldn't face getting another, and we spent months looking at other large pastoral breeds. In the end, we came full circle and now have Pyreneans 8 & 9. Because I suppose in a way we felt nothing else would ever match up.
So while I understand you feeling that another Basset just wouldn't be the same - and it won't - I would hesitate to opt for something very different, because when you've spent so much of your life with such a calm, steady breed, it may be that anything more active would drive you mad.
Sorry for the long post, but having also been a one breed person, this did resonate with me.
Good luck in finding your perfect dog and again, sorry for your losses.