It is not clear how Rambam arrived at the values he gives. When value of the movement in one day given by Rambam is multiplied by 29, 100 etc., the result is smaller than that of Rambam. The following table compares printed and calculated values: TODO
Although the value of the movement of the mean solar longitude in one day given by Almagest III 1 (H209) (which, rounded to seconds, becomes Rambam's value) is bigger, it is not big enough, and Rambam's numbers (for more than 10 days) can not be explained by performing calculations with the long value from Almagest and then rounding the results to the precision of the Rambam's values.
Tzikuni (TODO p. XXX) gives the algorithm of such reconstruction: add to the remainder as many times 360 as there were full rotations in given time period, and then divide. It also gives a value reconstructed from the printed values for 10,000, 1000 and 100 days: 59′8.33″, or 0.9856472 degrees, and the current "scientific" value of 0.9856473 degrees. It seems that origins of the Rambam's value were questioned by his commentators, including "Pirush". Value that can be derived from the tradition that 19 years = 6939 days 16 hours and 595 parts is 0.9856348.
This algorithm can be modified to produce an interval of possible values, taking into account precision of the numbers.
From the printed values it is possible to reconstruct the value of the movement in mean solar longitude in one day that Rambam used to calculate each of them:
Use it to calculate intervals for Rambam's values of the angular velocities.
Tzikuni quotes Rambam's value for 354 days as 348°55′15″, but calculated value as 348°55′9″, and notes that this "requires a little thought".
TODO About apogee, Rambam says "the same way", but doesn't give value for 1 day... Exactification requires extra attention, since there is no value for 1 day. SunApogee rambamValue and almagestValue.