The majority of plants will do fine in your hard water. My tap water is very similar to yours and except for some Rotala magenta (which reportedly prefers soft to moderate hardness) and Ludwigia 'cuba', everything grows well for me. And even the 'cuba' is coming along once I moved it to a different tank (same tap water, though).
Adding peat will acidify your water (lower the pH), but I don't think it affects the hardness any. Same with injecting CO2 into water, it'll lower the pH but the hardness will remain.
Your trickle filter may cause you to outgas some CO2, but you can compensate by upping the amount you inject (the penalty being the need to refill your CO2 tank more often).
Other than that your setup looks good. Have fun setting up your tank!
Adding peat will acidify your water (lower the pH), but I don't think it affects the hardness any. Same with injecting CO2 into water, it'll lower the pH but the hardness will remain.
Your trickle filter may cause you to outgas some CO2, but you can compensate by upping the amount you inject (the penalty being the need to refill your CO2 tank more often).
Other than that your setup looks good. Have fun setting up your tank!