Georg,
The water-cooled conversion is quite interesting, and certainly seems to be no amateurish attempt.
1927 600 EW, E/F28, and E/F29 has two prefix versions. EH is one. S/EH, where the S is the numerator and EH is the denominator under a horizontal fraction bar is the other. This is what your replacement engine is, though the 'S' seems to be worn away. The 'S' denotes 'Sport' and originally denoted higher compression aluminum pistons verses cast iron pistons, foot pegs verses foot boards, and I think drop handlebars verses normal touring handlbars (though not illustrated in the catalog.) So EH would be standard, and S/EH would be sport. By 1928, the standard became the E28 and the sport the F28 (with twist grip throttle), this continued into the following years' E29 and F29. EH and S/EH engines were allocated serial numbers from the same contiguous sequence.
Do not be supprised if you open up the replacement engine, and it has cast iron pistons, and not aluminum. My S/EH prefix F28 was on standard bores and it had iron pistons. There may have been problems with the alloy pistons (particularly if Douglas tried casting them themselves) and they were swapped out early on. Douglas was clever with cast iron, but their aluminum was not brilliant. They were better off when they bought in their pistons.
Inlet manifold, and I think also the carb, should be the same from the 600 EW through the 1929 600 sv models. Other than the prefix stamped in the crankcase, the 600cc sv cases are identical from 1926 to 1929. The sight glass oiler changed in 1929, but this change is limited to the timing cover casting itself. You could of course swap parts between your two 1929 engines if you wanted to retain the correct EH prefix cases for your E29, rather than the F29/sports crankcases.
-Doug