I wrote something like this in a comment, but thought I'd make a Fanpost.
Given the offensive futility, lineups need to be flexible, allowing hot players to get maximum at-bats, and also tailored, perhaps non-traditionally, to prevent stranding runners as much as possible. Here is my case for a lineup for the next few days, until Hill recovers and (eventually) Eaton returns.
1. Bloomquist --3B (Clearly, he is not a leadoff hitter. But he currently has an OBP of .418, and needs to be ridden while he is the hot hand. Parra is good at getting on base, but also swings at too many bad pitches to bat leadoff in my book. He also has a tendency to kill rallies with a TOOTBLAN.)
2. Gregorius -- SS (Gregorius tends to struggle under the pressure of being up with 2 outs, hitting only .208. Having him bat at the bottom of the order makes it more likely he'll be up in that situation. Keep him here unless his slump extends, then move him down or even bench him when Hill returns, if need be.)
3. Goldschmidt --1B (I don't think I need to justify this choice.)
4. Montero -- C (He's hitting over .300 in June, and providing plenty of protection for Goldschmidt now.)
5. Parra --CF (Has his highest average batting sixth, but fifth is where he makes the most sense to me. Wouldn't we all feel more comfortable with two on and Parra coming up as opposed to Ross, Kubel, or Prado.
6. Prado -- LF (Moving Prado to the outfield to fit in all the hot infielders. He might get benched soon, though, if things don't turn around. Batting him after Parra would be an improvement over batting him after someone slow.)
7. Kubel or Ross --RF. (Platooning Kubel and Ross seems the best move for the team at this point, unless someone needs an off day. I would put Kubel at 6 and Prado at 7, except it's good to mix up left and right as much as possible.)
8. Pitcher. (LaRussa used to do this, and here's why I think it's a good idea. Pennington is far from a great hitter, but is fifth among eligible players in OBP, at .312. He finds ways to get on base. But it does no good to have him get on base in front of the pitcher, unless there's less than two outs, and even then it requires sacrificing an out. And the pitcher isn't sufficiently worse than Pennington to hurt to move him up here. And since 6-7-8 slot tends to get out a lot right now, I'd rather have Pennington, getting on base 30% of the time, lead off the next inning, rather than the pitcher.
9. Pennington --2B. (I explain this above.)
When Hill gets back, the pitcher moves back to #9, and probably by then Bloomquist will have cooled somewhat and will move down to the bottom third of the order. Maybe try Gregorius in the lead off spot? Unfortunately, this team lacks a classic lead off hitter.