Sizing problem with vintage pattern--Need help!

[G J]

My mom asked me to make a sweater using a pattern from my grandmother. It's probably from the 60's. It's a set-in sleeve sailor-style cardigan. The sizing is completely different from current patterns (see below). Mom said to make size 16 (she usually wears an 8), but it's about 2" too narrow across the back. I've got the back of the sweater finished--or so I thought! My gauge is exactly the 11sts/2inches called for, but it's too small. Mom is 19" across the back below armhole shaping, but the sweater is 18".

So here's my question: Can I make the front of the sweater in a size 18 or 20 width (see below for a size chart for both Mom and the pattern) keeping the length even with the back and make it work? I know I'd have to re-do the shoulder shaping of the back, and I know the side seams would end up being a bit towards the back, but would it work? Or should I frog the whole thing?
Mom’s sweater measurements: (from a sweater she likes)
Chest (buttoned) 18 1/2 " Whole front at underarm
Width across back at underarm 20"
Width across back above underarm shaping 15"
Width across each front at underarm R 9 1/2 L 9 1/2
Length of each side seam R 13 L 13
Length from shoulder to lower edge Body 21 Sleeve 22 1/2
Length of sleeve seam R 18 3/4 L 18 3/4
Width across sleeve at upper arm Rl 7" L 7"

Pattern Info: Sizes
16
18
20
Supplies: Main color Ounces:
Contrast: 1 Ounce
#3 & #5 Needles
24
26
28
Blocking measurements:
36
38
40
Actual knitting measurements
Chest (buttoned)
39
41
43
Width across back at underarm
19
20
21
Width across back above underarm shaping
13 ½
14
14 ½
Width across each front at underarm
10 ½
11
11 ½
Length of each side seam
13
13
13 ½
Length from shoulder to lower edge
21 ½
22
23
Length of sleeve seam
18
18
18 ½
Width across sleeve at upper arm
14
14 ½
15
Gauge: 11 sts =2”; 7 rows=1”

Thanks in advance for your advice!