I'm not sure about cutting birches down, expecting a good growth of replacement tops. Birch trees tend to not respond well to removal of large branches - in this case you are talking about taking off the whole top. Otherwise, in general it is better to move a tree or shrub with a large root system free of soil than to cut the roots down to a comparatively small size in order to retain a soil ball. The exception, of course is the minority of species that cannot take even brief exposure to air. Since birches are sold bare-rooted, this is not likely to be a consideration here. Possibly your best bet with these specimens would be to keep the tops and dig and move them without the soil. Lifting, moving and replanting heavy soil balls with stumps sticking out of the tops does not strike me as "a hot idea". Depends on if it is really true that good, strong replacement trunks are liable to come out of these plants after such treatment.

I see the original post is over 14yrs old, but last post was 7days ago so clearly others are like me and still reading this post. Sad the OP never commented what they ended up doing. I'm in a similar situation but the area I'm looking to fill isn't near the house. Have deep yard and apx 10yrs ago planted a maple apx 7-10ft from our back fence that was supposed to be a fast growing tree but has only grown maybe 2-3ft tall in that time and mere inches in width. Talking to the place originally got it apparently had poor choice in where planted it as we planted it in the natural drainage section of our yard and we get a lot of runoff from the houses that sit higher then us. However being in Texas its dry more often then its wet. When it is wet its like the original poster posted can be wet/marshy for close to a week. Tree farm had some recommendations for the maple, my preference of their recommendations is to move it to a drier part of the yard. We have the room to do so would just bring it closer to the house and an established red oak we have and has handled the water well. Not looking to "fix" our drainage issue. Its doing what its supposed to keep the water from building by the yard and have a french drain that carries the excess water between the houses. The only thing the water impacting the maple does is impact this maple and make the grass a little swampy for a few days after heavy rains. Just looking for a tree that can handle this "temporary swampiness" and also our largely hot & dry climate and clay soil. Would like to put something in the hole digging the maple out of so asked the guy looking to have do the work for recommendations and he recommended Bald Cyprus, River Birch & Sycamore. In researching these three I found Weeping Willow which he said could also work. Which is why I'm posting here. Pretty much between the River Birch and the Weeping Willow. LIke the long growing season of the Willow, but think prefer the look of the River Birch. Didn't rule the Sycamore out but don't care for the seedlings it will drop as the red oak already makes a mess with its acorns. Several recommended the bald Cyprus and would like to note for those that don't have experience with an established Bald Cyprus. They are nice looking trees however in my opinion they are one of the messiest trees. Needle leaves & seedlings they drop are mess and worst of all they have what people refer to as "knees" that are the tree roots that pop backup in the yard which are a real hassle when cutting your yard. I would highly recommend against just for the knees, which would also be a hazard for anyone walking or playing in the yard. Reading others comments think might be now leaning the river birch or the sycamore. Several commented relative short life of the weeping willow which is a concern, though don't plan to be in the house long enough for that to be an issue. I think for our situation River Birch or deal with the seedlings from the Sycamore and go that way are the best options. Hope my post might help others. I'll try to remember to come back and post picture of the results once we buy and plant our new tree.

River birch will drop leaves when stressed, usually from lack of water. It's not because they are dieing, although it may seem so. They will leaf out well in the next spring. Before I realized that, and before I mulched as widely as mine now are, they would drop about half of their leaves by the end of summer - now they only drop a third, if that, if I don't water enough, and if it's REALLY hot for too long. Keep them watered, mulch them well, as widely as you can, no more than 4" deep, and with no mulch in the 2-4" next to the trunks. As said, container-grown trees should be fine, with a bit of extra care given to water needs. I have been told that many newly-planted trees do better without any other root competition in the first year, just being mulched. If you really NEED to see something other than mulch under them, most annuals are shallow-rooted enough that competition should be minimal.

I remember reading something that a small River Birch should have about a 3' diameter planting bed w/o grass and the planting bed should expand as the tree grows to at least 6'. I can't remember where I read that and I don't know how accurate that is. I also remember reading that Birches have a shallow root system that must stay cool and that they don't like having their roots messed with. I believe that if you plant the tree where there are already shrubs planted and you are not disturbing the tree's roots with various plantings, it would work. Keep the mulch at a good level and the roots should stay cool, keeping the Birch happy. You will need to give it water, though...can't plant it and forget about it. Last year, I planted 3 River Birch trees at my house. Two of them are next to the driveway in an area that only has mulch...no grass, and the nextdoor neighbor's small trees shade the roots some, as well. They are multi-trunk River Birch (each tree is one tree w/ 3-5 trunks...not 3-5 trees planted together) and seem to be growing well. The other one is a Heritage River Birch that I planted in a planting bed in the backyard. The planting bed is bigger than 6' and has plantings already in the ground, but not mature...but the plantings are not shading the roots of the Birch at all yet. I keep a good amount of mulch to keep the roots cool. It was planted in Dec 2008, so this is it's 2nd summer in the ground. It was about 8' tall when planted and it is already about 5-6' taller and more than twice as wide as when it was planted. European White Birches and Jacquemonti Birches are plentiful around here...with the former being overplanted. Both are too risky, as they are quickly falling victim to Bronze Birch Borer in this area. The River Birch is hardly seen at all around my area, but it is reported to be resistant, so I thought I would try it. So far, I love 'em. Good luck!