Yeah, I'm getting that [member=99988]SmallWelshBarn[/member] which is why I was previously suggesting putting the gates either side of the pathway rather than across the pathway, thereby dividing your field into 2 separate gated enclosures.
That would require you to move the pigs every now and then from one enclosure to the other and to provide water to the far enclosure, but it could, on the up side, help each enclosure to recover a bit between piggy visits and avoid the deep churned up mud across the piggy crossing place (as shown in your youtube vid).
Let's say, however, you put in pig-proof grids (not sure what pig-proof grid spec' would be, but I expect there will be one): you would need to find way of preventing the deep mud build-up across the path because slippery mud on walkers boots and slippery, wet metal grids might not go together too well (and I note the track-way is on an incline of sorts which might compound the issue of slipperiness). Also, all that mud would gradually build up in the grid wells. Plus you would need to ensure that dogs can cross or safely walk around by some means that prevents the pigs doing the same.
(I'm assuming it's not a bridleway!).
In summary, most pleased 'tis agreed your pigs are not 1st-gen' crosses and that pig-grids might be an option for you, BUT, if I were in your situation, I would simply gate off the two enclosures as per my starter sentence.