Mmm, warm-up in the home..... I run twice a day and go to the gym so plenty of opportunities to stretch. At home you could do skipping or up in the air bicycling perhaps - God they are lame suggestions. Or go for a brisk walk beforehand.
Regarding the training, random thoughts - your post misses out a bit of detail, such as:
- did your training change leading to tight hamstrings
- how do they feel after intervals
- what happens when you run with tight hamstrings
- what have you tried, 2 a days, changing workouts etc.
If I were you I'd try and run the day after even if your hamstrings are tight. Sometimes they will loosen during the run and a run will just be what you need. Try it as an experiment and do loops near your home so you can bail if necessary.
If that doesn't work and your hamstrings are tight the day after and preventing you from running I would cross train instead. If the tightness only lasts for a day or so no matter what the previous day's distance, then personally I'd bump up the mileage of my runs every other day in attempt to partially compensate for the reduced frequency.
Have you tried running twice a day to reduce the overall mileage done in one run to alleviate the symptoms? This certainly isn't ideal but if it increases the amount of time you are able to spend running it's better than the alternative.
How did your hamstrings react to the interval training? I'd have thought that would make it worse. I'd lay off those and only do upper aerobic zone running for your quality training.
How do you do your runs? Do you start off slowly and gradually build? That would be ideal to ease your legs into it.
As you know adjusting your training is only avoiding the problem. Do it for a short while but be aggressive with all the other modalities at your disposal.
It may be worth a week of getting back to basics. Plan a week of running 6 times, with no quality and no run longer than 5 miles. If you get through that, slowly add in the other elements of your running so you can really isolate the session which is the cause if indeed that is the problem.
If you are running easy and long runs at your target pace this is far from ideal. Meaning your target is a bit too soft or you are running them too hard. If it's the latter that may give you the answer you are looking for.