Here are some suggestions:
1) Cut one or two sheets of your 16x20 paper into four 8x10s;
2) Work with them to get another good 8 x 10 print, using at least f/11 and possibly f/16 on your enlarger lens. Record the time you use for the resulting best print, and note an area on the print that is a highlight area with detail - that is the area you will attempt to match in your 16 x 20;
3) Set up your enlarger (Beseler's site indicates the Printmaker 35 "can produce prints up to 11″ x 14″ on the baseboard or much larger when reversing the column and projecting on the floor") for the 16 x 20 size you want to print;
4) Position an 8 x 10 easel so that it includes the highlight area that you are attempting to match;
5) Open the lens two stops from the stop you most recently used for your smaller "reference" print. Use your test strip method to match the highlight using a #4 filter - the exposure time should be close to the time you used for your 8 x 10 reference print;
6) When you determine the correct exposure time for the highlights, do a test on another 8 x 10 section of the image that shows how the shadows will appear with the new #4 filter. If they look good use that filter. If they are too light, increase the filter number and recheck both highlights and shadows. If they are too dark, decrease the filter number and recheck both highlights and shadows;
7) Once you have both the shadows and highlights looking good in 8 x 10 sections that you have tested, move your attention to the mid-tones. Depending on the image, you may find that slight adjustments to the mid-tones may have the greatest effect on the results;
8) When you are happy with the smaller 8 x 10 excerpts for highlights, shadows and mid-tones, you can try a full 16 x 20, to see if the "whole" is different from "the sum of its parts";
9) Note that it is important to do the tests on the 16 x 20 paper (cut into smaller pieces) rather than paper that started out 8 x 10. Otherwise you may run into problems arising from differences in the emulsions.
Finally, I would suggest avoiding exposures as short as 3 seconds. They are hard to repeat, and give no reasonable opportunity for dodging and burning.