If you want stock that isn't inkjet coated, which is the only way you will get that slight sheen of magazine type paper, then you would probably have to go with a color laser printer that does 11" x 17". They are only four color: CYMK, but should do fine for what you want. Local print shops can usually do these for less than US$1 each. taples, for example charges 98¢.
I print posters on Canon Coated Matte 170 g/m² and Canon Satin 170 g/m² roll paper on Epson printers. Satin is probably as close as you will get to that low gloss sheen you are after.
Using an inkjet printer with uncoated stock gives very poor, washed out results.
For four or five a month, you are much better outsourcing.
Brian A