The top 64 go through from the first two days’ 36-hole stroke play over the famous Open venue and Panmure.
An indication of the task they face is that Marsh and Dean lie tied for 44th in the field of 288 while Bedale’s Daniel Brown – who played Panmure and is just a stroke higher with a 73 – is equal 73rd.
Jamie Bower (Meltham) and Julian Taylor (York) are one further shot back – Taylor’s score coming at Panmure – with Jonathan Thomson (Lindrick) on 76.
Shipley’s William Whiteoak will have been the most disappointed Yorkshire competitor. Having begun with three consecutive birdies at Carnoustie, an inward nine of 42 included dropped shots at his closing six holes as he carded 77.
Hull’s Steve Robins is on 78, two better than Daniel Wasteney (Bondhay) and six to the good of David Houlding, of Moortown, whose equilibrium may have been permanently disturbed by an opening double bogey six.
English Amateur champion Marsh went to the turn in two-over 38 then produced a three-birdie burst over holes 12 to 14.
He surrendered one of those gains to the 15th hole, but he and Dean appear in good shape to qualify with Panmure considered the easier of the two courses.
Dean’s round saw three dropped shots squared off by three birdies, and he twice showed his composure by birdieing the next hole after a bogey.
Brown – like Marsh, a member of Great Britain & Ireland’s provisional Walker Cup squad – was out in one-under 34 at Panmure despite starting with a five at the par-4 first, but came home in 39 for his 73.
Bower stood one under through six holes, but shed three shots at holes 7 and 8, and two birdies on the back nine sandwiched bogeys at 13 and 14.
Taylor, who was in the first group out at Panmure, was another to string together three consecutive birdies, but he will be regretting stumbling over the last two holes, both par-4s, which he covered in 12 shots.
Thomson was also one shot to the good against par after his first dozen holes, but would bogey five of the subsequent dozen.
Robins could not find a birdie in his 78 while Wasteney went seven holes before pencilling in his first par, his birdie at the fourth preceded by three consecutive bogeys and immediately followed by another bogey and a double.
Tuesday’s Yorkshire tee-off times – Panmure: 07:00 Steve Robins; 09:28 William Whiteoak; 09:50 Daniel Wasteney; 10:12 Jamie Bower; 10:45 Joe Dean; 11:07 David Houlding; 13:13 Jonathan Thomson; 15:19 Nick Marsh.
Carnoustie: 11:34 Julian Taylor; 13:13 Daniel Brown.