I don't know what your painter's objection to painting vinyl siding is. Vinyl accepts acrylic paint well. However, you must not use dark colors on vinyl, as vinyl is subject to warping when heated to as little as 130 degrees. Dark colors absorb heat and surface temperatures in the sun on a hot summers day could approach this temperature if painted with a dark heat absorbing color. Permanent warping of the siding could occur! Pick a color no darker than manufacturers are offering on their new vinyl siding.
Personally, I don't care for the look of formal brick when painted. "Common brick" lends itself more to being painted from an aesthetic stand point, in my opinion. Perhaps you just object to its natural color. If this is true, there are masonry stains on the market which can change the color of brick.
I think what you might be objecting to is the stark contrast of the white trim and siding to the red brick. Have you considered using a color on the trim? A muddy, tannish color might look good on the trim and/or siding. Dark black/green or deep maroon might be a good accent on the doors and shutters, especially if the red brick is retained.
Most of the paint manufacturers have computer programs which will allow you to scan in picture of your house and then put their colors on the various house surfaces.
Your house has a few architectural features that I don't care for. I personally would replace the ironwork trellisses on the front porch with wooden posts with appropriate colonial decorative trim.
The concrete trellis-like blocks are not particularly in keeping with the traditional colonial look of the front facade. Painting them with the siding/trim color would make them stick out less. Foundation plantings such as a few columnar arbovitae would also lessen their prominence.
Just a few thoughts for your consideration.