Waiting until you have your own home is a good reason to wait, it just depends on your situation and no one knows that but you and your DH.
Is there a greyhound group near you where you can volunteer some time each week? Walking them, bathing, etc. Even if it is a meet and greet you could help out, answer questions etc. Here are a couple I found.
GPA group
GreySave
Hemopet
I know of some folks with our group who could not adopt, but wanted to be around the greyhounds, and that is what they did. They became regular volunteers until they were in the position to adopt again.
Earlier this week I took my Teddy to a specialty vet clinic for an ultrasound and while there I was talking with a lady who told me that she and her DH had lost two greyhounds very close together and her husband did not want to adopt or even be around greyhounds because it was too painful for him. She, however, needed to be around other greyhounds in order to begin healing. She started coming to the kennel every Sunday for 2 or 3 hours and just walked the greys waiting for adoption. Eventually her DH was ready again.
I hope you are able to work something out that will be OK for both of you. I know how hard it is when we lose them.