Sounds like a similar situation to me last year. I put the spuds in , no weed killer, no manure, nothing, just rotorvaterd to a fine tilth, ridging plough and planted potatoes at 12 inch. The spuds did the business, the only weed that has had any effect is dockers. This time my main crop spuds are going in at 18 inch. Dockers still a problem but everything else in the weed department is minor. Other veg going in as well, if and when it stops raining.
Spuds are tough cookies, have faith in them, couch grass can affect them but let them work their magic. I was told that some farmers literally dug a hole and dropped the spud in, into fields or paddock areas they wanted to reclaim from grass and weed. The spuds conditioned the soil and the land was ready for working next season. Never tried it myself but I can believe it.