parking on slats

Normal slats - do you mean singles? Single slats are mostly classed as cattle bearing only. Most gang slats are 4T and upwards.

We have left machinery on slats before, but they are fresh gang slats rated to 10T.

Gang slats are usually 1.2m (~4ft) wide. I looked on McGraths and they don't have any data stating what axle loading they quote for standard slats. I think that from purchasing recently cattle bearing are 800kg, standard are circa 4T, overlapping with tractor bearing which are between 4.5T - 7.5T and heavy duty are 10T.

So really, you could have anything there, but if they aren't tractor rated, then you would be at the lower end of the scale. Would you be able to get the trailer onto the slats without rear of tractor going on too?

TBH - 15'6 is a fair width of a slat and would be at the upper end of slat widths, so you might find that it is cattle bearing only. If any of the structural engineers on here can advise, I think that a static axle load over a period of days/weeks is a totally different set of calcs to that for a dynamic axle load.

Unless you can find the dept definition of Standard and Heavy Duty which they use here:

and see if it was in place 12 years ago. A bit of a faff I know, but I'm not sure any of us can advise on this unfortunately as the axle loading of the slats is not known.