Don't tell anyone, but I used to be a toe walker, too.
Same basic problems, too. Before you go off and get all stretchy in the quads and hamstrings, consider that those things aren't all of it.
Considers also...
- tight calves
- poor ankle mobility
- tight hip flexors
These things all hampered (and to a degree, still hamper) my squats and deadlifts more than the quads and hamstrings did/do.
I spent a lot of time stretching my hamstrings, to no avail. Sure, they were a little tight, as were my quads, but stretching them didn't really help.
I spent a lot of my time focusing on lunges and lunge stretches, which do stretch both the hamstrings and the quads, but also give my hip flexors some help in loosening up.
I have and still stretch my calves religiously.
In the meantime, rather than skip the deadlifts, take a read of this article,
Mastering The Deadlift III, which goes over some of the alternatives to a conventional deadlift. Like rack pulls, to start. Then, progressing down to a sumo style deadlift, both of which can be better for people with flexibility issues.
As for squats, try widening your stance to see it that helps. I had to use a plate for a while, too. Eventually, I was able to ween myself off of the plate. And, I wear my shoes with the bigger heals to squat.