Bike type suggestion for packed limestone trails
No need to a full suspesion - waste of good money on these trails, you need $2K to get one thats half decent - however if you have got $2.5K burning a hole in you pocket, full sus will be more comfortable.  A Hardtail MTB is built a little heavier than a hybrid, but in the end, I doubt very much it would make a difference. 

What I would do is look at some cheap upgrades to your existing bike. Go to the biggest tires you can fit (Without going insane) 2" would be good - rim width and frame cleance need to be considered. No only comfort, you might want to consider a shock seat post. These are a often considered "poor mans softtail", but do not get the attention they deserve - they do take some of teh stress and shock loading off the frame and wheels. They are great for taking the small ( &lt;25mm ) bumps on these kinds of trail while remaining seated. 

If you decide to go for a new bike, a quailty steel hardtail MTB or hybrid would be my pick (unless you can afford carbon or titanium), with low travel shocks (80mm, no more than 100). A 29er (29" / 700C wheels) rolls better over the rough than 26" and are ideal for these kinds of trails