Jel, before you condemn your existing core cutter, it may just be a case of the diamond faces being glazed from cutting ‘soft’ materials (as hinted by Geordie). In the context of core cutting, ‘soft’ mean anything softer than standard house brick, so that would include materials like sandstone, limestone, thermalite block, aerated concrete block etc. What you need to do is drill at least 2” in hard material like concrete paving, concrete kerbing or engineering brick; this will restore the diamond cutting faces to their original effectiveness as if by magic.
As others have already said, but worth reiterating, the SDS tool holder is very inefficient when used in the hammer stop mode, a large core drill will quickly stress and wear the tool holder and ultimately destroy a 4kg SDS if it does not have thermal protection. If you suspect your drill of getting excessively hot, stop drilling, switch to the max speed range and run it flat out for least 5 minutes in free air to allow the motor fan to cool the windings.
As soon as you are able, get yourself a proper diamond core drill. They generally come in two forms: - 1) The conventional chuck type takes a hex arbour. 2) The threaded tool holder type takes a screw fit arbour. The former, allow you the flexibility of a standard drill. The later, higher torque of a direct drive at the expense of more laboured tool changing.
Of the chuck type the Makita 8406 is fine example, offerings from Dewalt and Bosch are better, but my personal favourite is the Milwaukee DD2-160XE.
Direct drive types are the professional choice however. The Marcrist DDM2 and DDM3 allow wet and dry cutting at fixed speeds. I have never felt the need for variable speeds when using one of these, I find them remarkably efficient when paired with the same make of core cutter, but some of my colleagues disagree. Most of the main players have top of the range models, with Hilti being the firm favourite with my work mates.
, amazing speed did a hole the other week for the first time in hard engineering brick double skin it took 4min or less 
