While I appreciate & understand what you're trying to do here, the cost, while not free, is negligible.
Suppose you're printing a 16x20 canvas print. Depending on demand, local markets, your calculated labor costs and a couple of other factors, you should be selling that print alone (frame/mat not included) for somewhere between $300 and $500. Perhaps even a bit more.
Even if your ink costs for that print are as much as $5 (which they won't be), that represents pennies on the dollar. If a ~$5 ink cost is going to cause a financial loss, you aren't charging enough in the first place.
Just sayin'...
Note: We currently have an Epson R1800 printer, using Epson Premium Luster & Premium Glossy paper and Epson inks (in those goofy/expensive 11ml cartridges) an 8x10 will cost around $1.25, an 11x14 less than $2 (paper & ink included). With the volume we put through that printer and knowing exactly which consumables it uses, it was an easy exercise to calculate the numbers. We also have an Epson 4800 and I have no firm idea of print costs, I just know it's far less than the R1800.