Some have mentioned Justin Upton as a possible substitute for Heyward. I'll accept that, if the financial savings is adequately invested elsewhere, and the Cards don't give him more than four years at the max.
Second is that need for a pitcher. Mike Leake, Wei-Yin Chen, and Doug Fister seem the best possibilities. Chen is as good if not better than Leake, and being younger, might still have some uptapped upside. Fister, after a down year with the Nationals, might accept a short-term contract to rebuild his value. Or Mark Buehrle, a heathly "innings eater," might benefit from both a change of leagues and a homecoming, if he decides he's not retiring. I find all of these options better than Scott Kazmir, who I think is overrated by many. A season-plus in Oakland doesn't wipe out a lot of past blemishes in my book.
Kazmir, though, as well as Leake and Buehrle, don't require draft choses due to QOs. That's some benefit to them. That said, the Cardinals draft late enough that it's not a huge penalty to pay.
Anyway, really, that's all the Cardinals need on pitching. A number 3 starter, or really, a 3/4.
Picture some combination of Adam Wainwright, Michael Wacha, Jaime Garcia and Carlos Martinez as providing the top two pitchers in the rotation for sure, and possibly the top three, the Cardinals are looking for a 3/4 starter, and even then, just until Lance Lynn comes back from his Tommy John surgery sometime during the 2017 season.
Waino generally seemed to do well in his rapid post-Achilles return at the end of last year. Wacha largely bounced back from his late 2014 shoulder issues. Garcia generally was healthy, by his standards. Martinez did have some arm "impingement" that shut him down at the end of the regular season, but so far, there's been no concern expressed beyond that.
A two-year contract for a 3/4 starter, or a three-year, if necessary, lets the Cards see what the longer term aging curve of Waino is, just how much upside Wacha has beyond his performance so far, whether Garcia can hold up another year, and what the team should do after that, and, assuming Martinez' arm is fine, what he can do after that.
Tim Cooney, who had a peak at the big club last year, Marco Gonzalez, who had more than a peak in 2014, and a sip in 2015, and Alex Reyes are all possibilities for sufficient improvement to see time in 2016, and make the big club out of spring training in 2017.
In other words, a nice pickup is good here, and, yes, David Price would have been great, but no overpay is needed. A "bridge" is what is needed; a Calatrava bridge is not a need, it's a luxury.
IF Heyward is resigned, my preference is Buehrle if he doesn't retire. He'd probably be the least expensive, and fit most into that "bridge" role
Third is improving the situation at first base. I'm not sure either Brandon Moss or Matt Adams is much of an answer. That said, don't forget that new backup catcher Brayan Pena can also play first. If somebody else on the free agency market is a better answer than Moss or Adams, that's all good. But, this is the third priority. If Heyward is resigned, then Stephen Piscotty is part of the answer, of course.
If the Cards need to spend some money here, getting a relatively inexpensive "bridge" as a pitcher means more money to spend.
Fourth is more middle infield depth. Giving some days off to Jhonny Peralta at short, while offering a RH bat option for Kolton Wong at second are both good. Aledmys Diaz showed some promise at the end of last year in Memphis, and had a very solid follow-up in the Arizona Fall League, where he played both positions. He may be the Cards' first answer there. They don't need to break the bank for Ben Zobrist, who's not worth bank-breaking money anyway.
The Gyorko trade addresses this; it's nice, but it's No. 4 on the list.
Fifth is tweaking the bullpen where needed. Assuming that Jordan Walden is back and healthy for a full year helps right there.