Whilst coppicing is without doubt an ideal way to favour many woodland species - the so called "gap phase" species that require relatively high levels of light on the forest floor - it is important to remember they are only one component of our woodland flora (and associated fauna). Many woodlands, particularly in the S.E. of England where coppicing was most widespread and continued longest, have artifically high numbers of these gap phase species, and following coppicing they respond dramatically with beautiful carpets of spring flowers.
Unfortunately, despite the arguments that a few retained standards help, these woodlands are typically very poor in the species that require mature growth.
Coppicing isn't always the most appropriate management choice. If you have individual stems of 40cm+ I think you might want consider if nudging this woodland in the direction of High Forest my not have more environmental benefits?
Deep sandy soils do not mean unstable trees - in fact quite the opposite. Well drained soils like these encourage deeper rooting in chestnut.
You could ring bark some of the stems on a stool. You have to remove a complete circle of bark at least 6" wide on Sweet chestnut (sweet chestnut is one of the fastest species at healing bark damage by callousing) . No extra risk of windblow of these stems for about 10+ years as chestnut is increddibly rot resistant, and the remaining live stems keep producing sugar which is sent down to keep the roots alive - so rot resistant stem held up by live roots = wind safe for at least 10 years.
By killing some stems you let more light to the remaining live stem which responds quickly with good growth. The advantage of the stable dead stems still being in place for a decade, is that they provide some gradually reducing wind shelter to the live stem - so it adapts to the change in its circumstances (i.e. by laying down varying amounts of tension/compression wood on the appropriate sides of its stem or butressing etc.)The shelter is gradually reducing as the live stems gradually overtop the dead stems growing out of the shelter of the others, and the twiggy bits of the dead stems are lost - so the wind exposure is slowly increased, at a speed the live stems can respond and adapt to.
Then after 10 years or so you could fell the ringbarked stems which will now be perfectly seasoned for fire wood- and have the advantage of being much lighter in weight.
This technique is only suitable for rot resistant species such as oak and sweet chestnut - definately not safe for birch, sycamore, beech etc.
(I've never done it myself with big oaks only chestnut - but by coincidence have just mailed someone who has done something similar with oak!)
P.S. In young woodland/coppice woodland natural cavities for nesting birds, invertebrates etc. are always in short supply. You can increase these with a cordless drill (ideally 24v) and one of these brilliant bits;
http://www.tlc-direct.co.uk/Main_Index/Tools_Power_Index/Drill_Bits_Wood/index.html
With these you can drill a hole, and then plunge in through the same hole at different angles to make a much larger cavity behind the small initial hole. Obvioulsly angle the hole so it won't fill with water - although where it's safe some water filled holes are important for the larvae of some hoverflies... Again this is a technique for rot resistant species - ideal for sweet chestnut, western red cedar etc.- otherwise you risk wind snap. (I've been doing this for over 10 years in Chestnut and haven't had a single stem fail - and have anecdotal evidence that great tits fledge more young than from birdboxes, and they're more likely to be used by nuthatches than the specialist woodcrete boxes offered at such high expense!)