I've found that if you blend it and refrigerate prior to injecting, it gets thicker.
If you want it thicker, I second the xanthan gum solution. You can find it in the gluten-free baking section of some supermarkets. It is pricey but a little goes a long way. It seems to work best if blended.
I tried to make my own pork phosphate injection because I didn't like the taste of the commercially available ones. It has been a failure to date but the xanthan gum worked as intended.
White Sox UDS, Black UDS, Weber OTG and Performer, Orange Thermapen