I like option A. It would be more work or more money than doing a slab sidewalk. Obviously you would be choosing the biggest project this way. You could always put concrete and finish later if you drop the sidewalk a bit where it meets the bricks(or grind it down later). The concrete placing labor is cheap. Not really much economic incentive to do it yourself .Maybe form it and place the reinforcement if anything.
The thinner bricks are called half pavers. If you don’t find them at RCP. Thompson Building Materials has them too. You can get them to match closely what you have if it has some kind of rustic or salvage look to them. Even Home Depot or Lowe’s might have them.
If your slab looks like it moves much with the season,and cracks in a brick patio would bother you, plan expansion joints and maybe some type slip sheet under too.
