Hi, mollie, without wishing to 'shut the door after the horse has bolted' so to speak, you made the mistake most people make when taking out any tree/large shrub by cutting it down to ground level and then worrying about the remaining stump/root. For future reference and for other 'viewers' the easiest way to remove any large shrub etc. is to remove the side branches, leaving as much of the main stem/trunk, tie a rope to the top and cut around the stump with a mattock whilst pulling on the rope and you will find it relatively easy to pull the whole thing over and out. But back to your present situation, the reason that the ground was dry was that the foliage of the conifer physically prevented the rain from reaching the soil and also the conifer would naturally have taken an enormous ammount of water from the ground in it,s own right but as its now gone you will be ok. Personally I would not bother with the drilling and application of chemicals etc. as the roots will eventually rot. Your only problem will be the physical ability to dig holes with the stump and roots still in the ground, so providing you 'plan' where you will plant so that you can dig holes you will be OK. Without knowing where you live, I would opt for prostrate evergreen shrubs in groups which will not only look quite attractive but be relatively easy to maintain and the following suggestions will also cover the ground qite quickly; Ceanothus thy. Repens. Rosmarinus prostratus, Euonymous 'Emerald and Gold'. 'Sunspot' or
'Emerald Gaiety' Hebe albicans, Leucothoe 'Scarletta' Erica carnea varieties etc. etc. and if you have not shredded the leylandii , which would have made a superb mulch for your 'new' planting, mulch the area with bark etc. for effect, to retain moisture and suppression of weeds (and to hide your stumps) Hope some of this helps,
Regards Lannerman.