Leaving Montrose you need to cross over to Ferryden,you can then either use the coastal path out past the lighthouse (and TGOC cairn) and follow the coastal route to Usan, or take the more direct route by road from Ferryden to Usan using National Cycle Route 1 https://tinyurl.com/yaq46lrv. Following the coast between Usan and Lunan Bay isn't really recommended, I would stick with route 1. There are great facilities at Lunan bay, a bunkhouse, a guesthouse, a great wee cafe, an official campsite and also wild camping opportunities https://www.lunanbaystays.scot/about If wild camping I would recommend the southern end of the bay. Note that the creek crossing the beach below Red Castle isn't normally easily forded. You can weave your way down to Auchmithie using the clifftops and backroads but it would be a very convoluted process in places, I would again consider using Route 1.

Thank you very much, Brian. It confirms what I suspected, that there would have to be some road walking heading out of Montrose and it's good to know that I need to plan to stay on the road till near Auchmithie. I finished at Lunan Bay a few years ago but had not realised how much there was there.

A lot of the clifftop/beach bits are passable and good fun for a days dog walk but the route often depends on crops, livestock and tide, there isn't a defined waymarked route the whole way. I wouldn't bank on a through route carrying a full pack and a tight schedule. The network of little backroads are very quiet though; Google Streetview will give you an idea of what they are like. Auchmithie to Arbroath is a good clifftop walk along a defined path and Arbroath to Dundee via Carnoustie and Monifeith, as you already know is straightforward. Carnoustie to Broughty Ferry is almost exclusively along the edge of the various golf courses. Once you are in Fife, the coastal path is a whole different well defined and waymarked story. I've never done any of it but an alternative to the Fife Coastal Path is The Pilgrim Way https://fifecoastandcountrysidetrust.co.uk/walks/fife-pilgrim-way/