Use a sealer pre painting, some you can spray on.
The paint won't bond the loose stone, and brush painting will pull more dashing off. The sealer will also help the paint stick better.
My attitude to works like your want to do is to do it right, use the best material solutions and hopefully get more years out the job.
We all have different ways of working, but since you mentioned dashing falling, and crumbly surface texture I would still suggest a primer sealer.
£25 for 4 litres v 60 m sq cover.
I'd blow out the idea of spray (pun intended).
A. To get the same coat thickness will need half a dozen passes
B. Over spray
C. Wind
D. Masking off windows, gutter, doors etc
E. From ladders
Buy the best paint you can, minimum spec trade smooth masonry.
If the dash is low profile a long haired roller works well, otherwise its a mid or large masonry brush (get one that holds a decent volume of paint) and off you go.
Reason to consider brush size, it that a large one can be counter productive if you end up with fatique after an hours use.
Something you might want to consider (well I do this in London property due to pollutants).
Get a large pump spray make up some decent strength sugar soap, spray the dashing throughly and leave for an hour. Then wash down with a hose on fine spray and a soft brush (steal the dustpan one). Allow to dry out for 24 hours.
This process gives the best start for the new paint, clean oils away, and will take off dashing that will drop off anyway.