No it isn't.
Well, you are lv 57. So if you are pure constructor - you have 57 toughness
+ 28 from indian feather hat
+ 40 from green shawl
+ 38 from fancy leather jacket
+ 31 from fancy riding boots
+ 5 from precise army revolver
Total 199 out of 235. So is it really a problem to do it even for a pure builder such as you?
235 gives 0 LP, you need 236. The precise army revolver requires level 58, so he needs a regular army revolver for +4 instead of +5. If he's done Kate's ring, as he should have, he has +2 more strength, for 59 toughness, so he has 200 out of 236. So all he has to do is spend $28,050 on the gear you mentioned, with my correction, plus respec 18 points of construction to appearance, for $2,430, assuming he hasn't done any other respeccing, for a total of $30,480. Respeccing the appearance back to con will cost another $5,670 for a total of $36,150.
Now all he has to do is do a 77% danger job with 1 LP for about 11 30-minute shifts (7 with premium) to get a song book, yeah, no problem.
Lincoln's top hat: +42
Red shawl: +42
Red cotton jacket: +42
Pilgrim's shoes: +29
Total: +155 LP
Pilgrim's hat: +6
Silver cross: +5
Pilgrim's shirt: +26
Pilgrim's shoes: +29
Total: +66 LP (+96 LP for 4 pieces of set)
Pilgrim Set
2 pieces: +5 LP
3 pieces: +15 LP
4 pieces: +30 LP
5 pieces: ???
If 5 pieces give +60 LP, that gives you a total of 126 LP, 29 less than using regular gear (including the 1.19 pilgrim shoes). If 5 pieces give +90 LP, that's 156 LP, or one more than regular gear. If you haven't respecced the appearance yet, you're down another 54 LP from the 18 points of con that you're down, so the full pilgrim set would have to be +143 LP towards construction to equal the LP you get from the regular gear, and I really doubt 5 pieces give you 5 times the LP bonus of 4 pieces.
$36k is a lot to spend to lower your building points.
Don't bother unless you want the song book for other reasons!