Morris shot 71 72 for a one-under-par 36-hole aggregate to lie tied sixth, albeit some 11 shots back of the runaway leader.
Bramhall’s Bronte Law followed up her opening 63 with a 69 to lead by 10.
Morris amassed eight birdies over the two days, compiling half of these at the third and ninth holes by playing them in six in each round.
Hallamshire’s Holly Morgan is tied 15th following rounds of 71 and 76. Four birdies were the foundations of her first-round score but she could find only one in the second.
Ellie Goodall (Selby) totalled 150 (72 78) for a share of 22nd spot. Two birdies offset two bogeys in her first round and after four bogeys in round two she recorded a 2 at the 208-yard par-3 14th, but it unfortunately preceded a card-scarring 7 at her next, a 442-yard par-5.
Olivia Winning, of Rotherham, is one shot further back (74 77), tied for 25th. Her first round contained three birdies, but her second only one, at the 15th, plus six bogeys.
Three Yorkshire players were unable to make the cut, which saw the top 32 and ties progress to the final 36 holes.
Fulford’s Charlotte Austiwck totalled 152 (78 74). She scored 10 consecutive pars at the start of round two, dropped two shots at 11, immediately retrieved one at the next but then bogeyed 16.
Hannah Holden (Lightcliffe) trimmed six shots off her first-round 80 for a 74. She had two double bogey 7s in round one – at the 454-yard seventh and 442-yard 15th – but showed character to hit back with a two-over score which included three birdies.
Ganstead Park’s Abigail Smee (80 79) was unable to mark down any birdies, but scored steadily save for two double bogeys, one each round.