Hi Herding Cats, and bless your heart for taking in this little guy... I know how rewarding it is to see them emerge from their shell. 
I've been reading the thread and see that you are thinking about introducing him to a walk outside. Be careful (I know you will be!) and make sure he is completely secured by lead and harness, because beagles- even very frightened ones- tend to bolt. And they are FAST!
I also had a thought for you, that has so far helped every timid dog we've ever had.
Play hide and seek. Just you and him (put the other critters up for 15 minutes or so.)
Get down on the ground in front of him, tell him to count to ten, and then turn and crawl away as fast as you can, and hide behind a doorway or somewhere obvious where you can still see him. Then start playing peekaboo, by popping your head around the door, and then hiding again. Be patient- he will likely get up and find you.
When he does- laugh, give him a quick scratch, and crawl into another room. He may run back to where he started from (safe place) but no matter- do it all over again. He should get the hang of the game in no time.
It's been a really useful tool for us.
Good luck with your sweet boy. It sounds like he's found a home.

I've been reading the thread and see that you are thinking about introducing him to a walk outside. Be careful (I know you will be!) and make sure he is completely secured by lead and harness, because beagles- even very frightened ones- tend to bolt. And they are FAST!
I also had a thought for you, that has so far helped every timid dog we've ever had.
Play hide and seek. Just you and him (put the other critters up for 15 minutes or so.)
Get down on the ground in front of him, tell him to count to ten, and then turn and crawl away as fast as you can, and hide behind a doorway or somewhere obvious where you can still see him. Then start playing peekaboo, by popping your head around the door, and then hiding again. Be patient- he will likely get up and find you.

When he does- laugh, give him a quick scratch, and crawl into another room. He may run back to where he started from (safe place) but no matter- do it all over again. He should get the hang of the game in no time.

It's been a really useful tool for us.
Good luck with your sweet boy. It sounds like he's found a home.