I didn't give an opinion about Epcot, just DHS.
I agree that walking to an Epcot resort would be a good option.
From DHS the walk to the Epcot resorts is not all that short in my opinion, but it is doable. The boat would be faster but you do have to wait for it. And then you need to get to the bus area at your chosen resort. If you're in a hurry this may not be the best choice, but if you want to explore the pathways (walk or boat) from DHS are lot of fun.
With SSR, unless you already know the property and where best to get off the bus, my opinion is it might not be the best choice. Here's why...
Last year I tried going from AK to SSR to get to DTD because I knew SSR was close. But once I got to SSR I got off at the first bus stop, realized I really didn't know how to navigate to the DTD walking path, and waited a good 20-30 minutes more for the DTD bus.
Maybe it was just me, but I wished I had taken the AK bus to the AKL and gotten the direct DTD bus from there. I hopped on the SSR bus because it showed up first and I knew it was close to DTD.
I seldom recommend heading to SSR from a park in order to get to DTD. That resort is huge and it can be confusing to get around. And then, you still have the walk over to DTD.
If I were at either DHS or Epcot, I would head to an Epcot resort. If at Epcot, I would walk over to BC and take the bus from there. The walk is about 8 mins from the International Gateway.
If at DHS, I would walk to BW...takes less than 20 mins. The boat takes about the same time, once you are on the boat and it leaves the dock. The wait time for the boat to come can be up to 15/20 mins.
If going to Pop, you have to walk to the bus stop (at DHS), then wait for the bus, then ride to Pop, then wait for the DTD bus to come. If there are no waits involved, then sure, it's quicker. But, no waits seldom happens. So, you have the walk to the stop, about 5 mins, then a possible wait of 15/20 mins for the bus to come, then a 10 min ride to Pop, then a possible 15/20 mins wait for the DTD bus to come and the subsequent ride.
Now, if you're not in a hurry, I would head to POR, and take the boat to DTD from there. Very nice way to go, if you aren't in a rush.