Can you describe your boiler (model, or input/output BTU), pumping, and zone control configuration a bit?
One potential explanation for this type of behavior in a high thermal mass system would be a cast-iron boiler with a low-temp limit that stops the pump when the temperature is too low. This type of system typically inhibits the pump from operating during a call for heat until the boiler temp is 15-20F above the low-limit control. On an initial call for heat it waits, the pumps start and deliver some hot water to the rads, but the large slug of much cooler return water cools the boiler to the low limit, causing the pump to stop, only re-starting when the boiler is back up to temp.
When the pump re-starts the return water is then already a bit warmer than on a cold start- it may still be cool enough to cause the pump to trip the low-limit again, but it takes a bit longer on successive tries.
If that is what's going on, this can be corrected with some near-boiler plumbing with "system bypass" branch that mixes boiler output with the return water to ensure that it never trips the low-limit (that's a good idea on any high mass radiation system when the boiler is not tolerant of cool return water temps.) A cast-iron gas boiler can cut it with return water as cool as 130F (though you may have flue condensation issues in terra-cotta lined masonry chimneys at that temp) but with oil-burners 140F would be the low limit. If your boiler has adjustable aquastat controls for the high & low limits ( or a high-limit with adjustable differential temp ) you might be able to tweak it into a nicer behavioral by maximizing out the difference between high & low limit settings without re-plumbing anything, but that's something of a long shot.
In almost any of these system total volume in the radiators is large relative to the volume in the plumbing, and just re-plumbing some 3" pipe sections for 1" isn't likely to affect the behavior.
There is no payoff in energy bills by making these adjustments. If you can lower the operating temperature of the system 10F without creating condensation problems and it still keeps up that can save you maybe 1-2% for every 10F it drops due to lower distribution losses. Insulating all of the distribution plumbing (including all the near-boiler plumbing) with R4 fiberglass (~1" wall thickness) would also reduce both standby loss and distribution losses, and has at least some long-term payoff. (The half-inch wall stuff sold in box stores is both overpriced and underperforming. You can get much better values buying pipe insulation online.) The foamy pipe insulation use for potable water plumbing won't cut it- the temperature ratings are too low for high-temp heating systems.
The rated temperature limit for PEX is 180F, which would put a temperature constraint on how you operate the system. Most cast iron boilers are capable of operating at 210-220F, which is enough to degrade the PEX fairly quickly. Excursions even as high 200F isn't going to affect it much (other than void any imlied warranty) but above that would be imprudent.