Hi and welcome to NGA!
Your Crepe myrtle is definitely desperate for light but thankfully Crepe myrtle is tough and hard to kill.
Here is what I'd do (but others may have a different method on the best way to do this) ...
First of all realize that this year will be only a growing season. The next thing you want to do is take a shovel and make a ring around the trunk of the trees about a foot away from the trunk all around - don't dig under, just around. Now leave it alone for a few weeks and see how they react to having their roots chopped up. If after a week they don't look stressed, (If they do looked stressed, just leave them alone until they recover then dig them up and move.) cut the main trunk to about 3 feet high, dig it up the rest of the way and plant it in its new location making the new hole a half size bigger than the root ball. Put some good potting mix in the bottom of the hole and place the plant on top making the top of the root ball almost even with the top of the hole and add the potting mix around it and on top then tamp down to secure the plant.
In a few weeks you should see new growth coming up from the roots and hopefully some new growth on the main trunk. If it looks like good growth on the main trunk, then cut all the new shoots coming from the roots. If the main trunk is not sprouting then cut it back to about a foot and choose the biggest and healthiest shoot you see and cut all the rest. If you're ok with a bush then let the sprouts grow.
Since it's a new house and garden, the described method above is the safest and best way to move established plants.
I also wanted to say that being a new garden, don't make any major changes for at least a year until you see what the light does and what's in there. There may be some dormant hidden gems you'll want to keep and or move.