With the exception of the armatige i don't see how they can. Pets may not be OMG levels of DPS, but they're at least as potent as aft turrets. So this thing with Sensor analysis should have no issues hitting the same base DPS numbers. Might not keep up with abilities in, depends on how much the pets add over and above the turrets, but it's not going to be a significant drop off any way you look at it.
First, you're severely overestimating sensor analysis. It's not bad, and against gates and tac cubes or in PvP it might be a real factor, but most of the time in PvE you just don't get the time for it to stack up that much, and it has no effect on secondary targets if you're using AoE abilities. It's already pretty safe to ignore it with a Fleet Recon Sci, throw in the DHCs to speed kills and it's not going to be noticeable.
You also can't talk DPS without looking at abilities. According to the Starship Weapons Calculator even an escort won't get much above 3.5k DPS without abilities, and 4k is sort of the minimum that's acceptable for an Escort build. I've even heard of people measuring 13k with Gurambas. You get there with abilities, mainly tac abilities, and the Vesta will max out at 1 less of those than an escort, with only 1 instead of 2-3 at LtC or higher. Also, if you go that route EPtS takes up all your eng abilities, which means most of your 4 sci abilities have to be heals. Ultimately, the Vesta will not quite match an escort by trying to imitate one.
Cruisers get their DPS from chaining EPtS and EPtW, which lets them keep all their power levels very high without sacrificing tanking or other damage dealing abilities. To chain both of those the Vesta would need to put the LtC on Eng, and that means it doesn't get the DPS boost from heavy tac abilities and has to devote as many sci abilities as possible to heals, putting it in a cruiser ballpark, maybe with a little more DPS and a little less durability.
Yes, the Vesta is absolutely more powerful than other sci ships, but when you really get into the nitty gritty of trying to build it, it's not superior to current escorts and cruisers, just different.