I've never resigned anyone midseason for anything less than fair value. Frankly, its usually better to wait and sign em offseason for that kind of contract.
Generally speaking, I've taken a different approach to re-upping players. In years past, it was smarter to only re-up starters midseason and anyone else offseason. This year, I'll re-up anyone who a)won't turn 28 by contracts' end or b) won't regress past 75 OVR by contracts' end.
A depth FA will often sign if the total contract value exceeds fair value. Offseason: Instead of offering a depth guy $1.25 mil/1.0 mil bonus (2.25 total), offer 2.45/$0 bonus. It'll show up as ~ half likely (40ish pts), but FA weeks 2 and 3, you can generally fill out your 2nd string this way. If you draft like crap, you've got solid depth. If its a great draft, cut these players with no penalty.