The crewel work I have done has always come in kits. I'm currently working on stuff from the 80's. I am replicating a piece I made for my son for my GD. I have two identical ones to do and a complementary third piece for my DD.
That said, the fabric is not a twill, but a 100$ cotton. It's not woven too tightly, but evenly. There is also an even weave available I've seen at places like Michaels too. And I would say that my fabric is probably about that weave. I haven't looked at the one at Michaels lately, but I think it would work. I would suggest either trying the linen that is use for counted cross stitch or a good 100% cotton fabric. Kaufman's makes a line that would work well for crewel. The linen used for CC comes in different stitch counts, so you could go with a denser count.
Also because crewel upholstery is something I have seen made, you could check with an upholstery store for the fabric. You don't want too heavy of a fabric though. It may also depend on what your finished piece intends to be and what kind of yarn you are using.
I just did a search for crewel embroidery and I can see why you say twill. I would try a good quality quilt shop and ask them for Kaufman 100% Kona cotton. I like to touch and feel before I buy, especially if you are looking for a particular type of fabric. But here is a link to
Hancock's. They carry it. I personally love Kona cotton. We ( we being me and DD) have embroidered on it with cotton floss, but I have not tried wool, which then makes it crewel.
Good luck, HTH,
Linda