Bob, you need to understand that the rim you have is not a 700C rim and most 28" and all 29" tyres have the same internal diameter as a 700C tyre so they will not fit on your particular rim.
If you look at the following list of 28" Tyre information copied from 
schwalbetires.com you will see that the majority of these 28" tyres have a 622mm inside diameter, but the ones that 
should fit your rim are
 635mm (shown in bold below)18-622   28 x 3/4   700 x 18C
19-622       700 x 19C
20-622   28 x 3/4   700 x 20C
22-622   28 x 7/8   700 x 22C
23-622   28 x 7/8   700 x 23C
25-622   28 x 1.00, 1 1/16   700 x 25C
30-622   28 x 1.20   700 x 28C
28-622   28 x 1 5/8 x 1 1/8   700 x 30C
32-622   28 x 15/8 x 11/4   700 x 32C 700C COURSE
35-622   28 x 15/8 x 13/8   700 x 35C
37-622   28 x 1 5/8 x 1 3/8   700 x 35C
40-622   28 x 1.50, 28 x 1 5/8 x 1 1/2   700 x 38C
42-622   28 x 1.60   700 x 40C
44-622   28 x 1.625   700 x 42C
47-622   28 x 1.75   700 x 45C
50-622   28 x 1.90, 28 x 2.00    
60-622   28 x 2.35    
32-635   28 x 1 1/2 x 1 1/8   770 x 28B 700 x 28B 770B COURSE
40-635   28 x 1 1/2,  28 x 1 1/2 x 1 3/8   700 x 38B 700 x 35B 700 Standard 700B Standard
44-635   28 x 15/8 x 11/2   700 x 40/42B28-642   28 x 1 3/8 x 1 1/8   700 x 28A
37-642   28 x 1 3/8   700 x 35A
If you place a straight edge on the top of your new rim it should produce a gap of ~13mm between the straight edge and the rim of your old wheel when placed side by side as shown in your photo.
If the difference is as much as 20mm it might even be a 700A rim which would require a tyre with a 642mm internal diameter, and I couldn't find any of those!From what you have said, I suspect you may have a 28" rim (700B) instead of a 700C, as some of the 28" tyres have a slightly larger inside diameter.
A 28" x 1 ½" (700 x 38B) tyre has an inside diameter of 635mm.
There are very few tyres that are likely to fit your 28" rim, but I think the 700 x 38B tyre in the above link should fit your wheel and was the cheapest I could find 
(£12.60 including £2.99 delivery) but the supplier 
(Acycles) is located in France.
The only suitable tyres I could find quickly on the net in the UK were at 
SJS Cycles and the cheapest of these is £16.99 including £5.00 delivery:



           £27.99                           £24.99                              £11.99             
Click for more detailsI can't explain why the postage cost is 67% higher to have it delivered within the UK than it is to come across from France. 

Anyway, I hope this has helped you to understand why you 
"failed miserably to find a tyre that will fit".
Contrary to what you might have logically expected, a 29" tyre is not necessarily larger than a 28" tyre! 
Alan