In 1601 Godunov accepts the Sapieha proposal and becomes a king of the united Polish-Lithuanian-Russian union ( Unia Troista ).
In OTL russians with under 10 million population reach the Passific coast by 1640es, and Alaska in 1780es, and reach for Hawaii and California in 1810es.
In TTL the nearly tripled resources of this Polish-Baltic-Russian ( cossack! or "ruthenian" ) empire accelerate and amplify this "drang nach Ost" several times: Pasific in 1640es again, but Alaska, Hawaii and California in 1680es. Alaskan and Californian gold discovered in early 1700es. Imagine PLR's Eskimo "cossacks" expanding into Ruppert's land ( Why not all of Polynesia, New Zealand and Australia, too - by 1750es... Patagonia and Antarctica... early 1800es ). In the beginning of 19th century the clash-splash of the westward ( polish-russian ) and eastward ( brit-french )expansion waves across N.America shall be inevitable.