Eliminate one of the (unidentified) amps, for starters
One amp is usually more that adequate if properly selected. Two amps are only needed under very, very unique situations and, too often, cause new problems.
The Monster power bar is largely irrelevant for any reception concerns unless it happens to be defective. No evidence of that.
Multi-tuner Tivo's usually have their own internal amp prior to the splitter that feeds the individual tuner sections. That would make three of them (if incorporated) in your case....
Different receivers, including Tivos, have different capabilities. My suspicion is that your new Tivo is slightly more susceptible to strong signal overloading than was the old one. You'd have to contact Tivo and see if they would answer that question (doubtful).
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