It is not about overkill, but it is not efficiently placed.
First, use D2PAK LM3x7, SMD. Place the vias right outside the package, in the soldermasked region. Make 4-5 row of via, closely placed together. More rows have very little effect. Dont cover the vias with soldermask, actually after an isolation of say 1mm around the package, leave off the soldermask. you can dissipate 1W on around 2000 mm2 without trouble.