Dear Lindylou,
I have a simpler, albeit radical and potentially controversial, solution to the cart path problem - don't have them!
For admittedly mainly historical and pragmatic reasons British courses tend not to have carts - and even fewer have cart paths.
It could be said that, with the exception of providing for those who would otherwise not be able to enjoy a round, carts tend to undermine the spirit of the (4-ball) game as played by the typical club golfer. A 4-person cart is rare for obvious reasons, so the fundamental social element of the game is undermined by carts. Further practical difficulties arise when the occupants of the cart are respectively a hooker (!) and a slicer (not uncommon and hence the expression “Catholic Golf” - a cross (across) here and a cross there. A devout Catholic friend of mine finds this amusing so I trust it will not cause offence.)
My own opinion is jaundiced by the following experiences:
Being in a 4-ball on a weekend outing where our companions/opponents failed to navigate an unguarded bridge thereby pitching their cart in a narrow, boggy ditch. (That alcohol may have been a contributory factor was never established.)
On a similar occasion I witnessed a cart taking off into a blind hollow to the detriment of the vehicle, the course furniture, the erstwhile onboard equipment and the subsequent mobility of the driver and passenger.
Whilst enjoying a friendly but keenly contested after-work inter-office match we happened upon a group of “professional” footballers (trans. soccer) by turns hacking and moto-crossing one of the most scenic courses on the banks of the River Clyde. As is the wont of those with more money than sense, they quickly tired of this banal diversion and abandoned their round at the 7th to the relief of all concerned.
And 2 years ago my nephew returned from a weekend away with his friend and his well-heeled but convivial parents at a well known time-share resort in Northumberland with the following verified story: in a briefly unsupervised, and nearly fatefully embarrassing moment, the two boys boarded a cart parked on a slope in the car park. Cue an admittedly untypical Dennis-the-Menace moment which, had it been recorded, would be on YouTube. It wasn’t long before the cart was careering backwards and out of control in the general direction of ostentatiously prestigious motor vehicles, the prized possessions of two of Scotland's most illustrious golf professionals. By chance alone the cart found the small gap between the cars and came to rest in what had been an immaculately tended flowerbed.
Conclusion: no carts > no paths > no problem!