The microscope show in the photographs on pp. 16 and 92 of Bruckner's biography of Goudy (1990)  are Spencer brand microscopes (under magnification, you can just make out the label by its shape and part of its lettering). The Spencer Lens Company (later purchased by American Optical and marketed as AO Spencer) was one of the major manufacturers of microscopes in America from the late 19th through the mid 20th century.
This particular microscope could be one of several relatively similar Spencer monocular microscopes from the period.  (Goudy became blind in one eye, so a binocular microscope would have been of no use to him.) It has both coarse and fine focusing and a graduated drawtube (you can just barely see the graduations in the Bruckner/Cary photograph). It is equipped with a single objective (not the turret of three objectives more common even at that time). Goudy has removed the microscope's stage and added a shop-made light (screwing it on where the stage is usually attached). This microscope must be equipped with a micrometer eyepiece (I say "must" because Goudy is doing micrometry with it but there is no evidence of any other apparatus. In a photograph of this resolution you can't distinguish a micrometer eyepiece from an ordinary one.)
If I were to try to match the photographs of the pre-1939 instrument to Spencer / AO Spencer catalogs, I would hazard a guess that it most resembles the Spencer No. 25 or No. 44 (hospital or general medical microscopes; they differ only in the internal construction of their fine feed mechanism) or No. 64 (a high-school and college botany/zoology microscope). Here is an image of a Spencer No. 44-H. 
(The image above links to a 2048 pixel wide JPEG version, which is quite useful but still reasonable in size. Here is the original 1200dpi full-page scan as a PNG (8080x11961 pixels, 136 Megabytes): spencer-microscope-no-44-H-6pg-brochure-M15-21-1200rgb-01.png )
The microscope shown in the photograph on p. 115 of Typologia may be the same microscope (or at least a very similar Spencer microscope), but it has been fitted with a "filar micrometer" eyepiece.  This is visible as a knob (with a horizontal bit behind it) just below the top of the microscope. 
The post-1939 microscope shown on p. 119 of Boone's article is a simpler microscope (coarse adjustment only) of unknown brand (but it could well be a Spencer or AO Spencer.  It is fitted, very obviously, with a filar micrometer eyepiece.
I do not yet have a freely reproducible image of a Spencer filar micrometer, but here is a very similar Bausch & Lomb unit: 
In other words, Goudy employed good but standard school and general-practitioner medical grade optical inspection equipment minimally adapted to his workshop. I am aware of no record of him using anything fancier (such as an optical comparator).
One is from Advertising and Selling (May 1939) , p. 38:
(The image above links to a 2048 pixel wide JPEG. Here is the original 1200dpi PNG scan (4730x6919 pixels, 56 Megabytes): advertising-and-selling-v032-n06-1939-05-p38-panel-06-1200rgb-goudy-type-recrop-4730x6919.png )
The other is from A Half-Century of Type Design and Typography. (1946) , where it is the frontispiece of vol. 1.
(The image above links to a 2048 pixel wide JPEG. Here is the original 1200dpi PNG scan (4128x6232 pixels, 40 Megabytes): goudy-half-century-1946-v1-1200rgb-frontis-goudy-at-microscope-recrop-4128x6232.png )
It is an inspection microscope mounted on a stand. It is not possible from the photograph to tell what brand of microscope it is or with what accessories it is fitted. The Advertising and Selling image is from 1939, and so is probably pre-fire. The Half-Century image is from 1946; it isn't clear if it is pre-fire or post-fire (but the hint of a pitched roof in the upper right of the image suggests pre-fire).
There is an important but unresolved issue in Goudy's micrometry. Because they are measuring a virtual image within the microscope, both types of ocular micrometer (the regular micrometer eyepiece and the filar micrometer eyepiece) must be calibrated against a "stage micrometer" (a finely graduated scale located on the microscope stage).  But Goudy removed the stages of the Spencer microscopes that he used for examining matrix cutters (and re-used the screw holes by which it was mounted for the light source in his pre-1939 instrument). His measurements, therefore, must have been uncalibrated and, despite his statement that he worked to 0.000,2 inch, were probably not accurate. Given the importance he attached to these measurements, this is unfortunate.
2. See for example the 1924 Spencer Lens Company catalog (or any of several later Spencer catalogs) online on P. S. Neely's website at https://user.xmission.com/~psneely/Personal/Microscope.htm
5. For a good explanation of this kind of micrometer eyepiece, see the American Optical Corporation Reference Manual "Filar Micrometer Eyepieces." This is online on the P. S. Neely's website at https://user.xmission.com/~psneely/Personal/Microscope.htm (though note that it dates from 1971, several decades after Goudy.) For a more contemporary reference, see pp. 300-301 ("Filar Ocular Micrometer") of Simon Henry Gage's book The Microscope. Ultra-Violet Edition [15th edition] (Ithaca, NY: Comstock Publishing Co., 1932). For convenience, here is an extract of the filar micrometer material from Gage's book: gage-the-microscope-15ed-1932-0600rgbjpg-extract-pp-300-301-filar-ocular-micrometer.pdf
Simon Henry Gage's The Microscope, 15th edition, is in the public domain. The extract from it here remains in the public domain.
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