Reconstructing History sells downloadable, historically accurate patterns for garments & accessories, including Pilgrim garb. For about 1/3 of what you'd pay for tissue-paper dressmaking patterns, good for 1 or 2 uses, you can download a PDF, have your local office supply store print it on large-format paper or print it yourself (see photo) and make any and all versions as often as you like. Reconstructing History also includes advice on altering the "look" as desired.
Below you can see pattern RH104 (Men's & Women's 1600s Shirts and Shifts - companion not included), my printed pattern laid out on the dining room table and test-fitted with removable tape, then the 28 sheets taped together more permanently with packing tape. Finally, you'll see some cut-out individual pieces.
A few things to point out: My printer did not print the last inch at the bottom - I had to tape on 4 more sheets of paper and draw it by hand. Also, you will see where I had to cut off some of the overlapped paper to reveal important sewing terms (like "fold") on the next sheet. Also, the online ordering instructions say to expect an email with a link to download the PDF but no email arrived at my end. I did find the pattern waiting for me in "My Account," though. Finally, heed the designer's warning to read the instructions often and carefully because even a garment this simple was not constructed the same way we make them today.
Next up: Where do you get historically accurate cloth?