I think your original lamps may have been producing sufficient light but the optics look likely to be much wider than the 38 degree beam angle you need. Even if the optics on the LED do something like that, there is a diffuser on the front which would spread the light out again. The final lamp you found appears to be a COB design with better optics for a spot. Less light overall, but perhaps more light where you want it. Of course the Integral LEDs might not be producing the lumens they state, or may not function well on your transformers.
LED colours are not always consistent even within a particular brand. 2700K is typically closer to a regular incandescent than a halogen. LED "warm white" is typically closer to halogen white than incandescent white, but not always. Warm white LEDs do have a colour balance that is more "yellow" than incandescents or halogens even when the colour temperature is identical. The traditional lamps have more orange and red and less yellow and blue than the LEDs. There is never an exact match without buying prohibitively expensive lamps, just look for the ones you like best. Some look pinkish, especially with the cooler whites, some seem excessively yellow. Colour problems are accentuated with spots because they tend to shine directly on the things you look at rather than getting bounced around the room and "evened out" on different surfaces. Cheaper LED spots may also show colour fringes because the blue LED and yellow phosphor are different sizes and emit in different beam patterns.
