The thing that may be hard to understand if you've grown up in a fiat-currency world is that prices moved in both directions, not just one. The periods of high inflation you name are real, but they were generally compensated by subsequent periods of deflation, except for the case of 01947.

Fiat currencies are often stabler than commodity money, but they very rarely deflate. Bitcoin so far seems to be acting a lot like commodity money in this sense; in the sense of prices rather than the money supply, it has currently inflated about 230% from its peak in value earlier this year.

The Warren–Pearson wholesale price index is the one usually used for measurements of pre-WWI inflation in the US, at least by people who don't simply use the price of gold; it is plotted on https://newworldeconomics.com/the-warren-pearson-index/ and appears to be about 80 in 01776 and about 80 in 01891, where they've suspiciously cut off the price data.

Warren and Pearson's book is apparently in the public domain in India and is available at https://dspace.gipe.ac.in/xmlui/handle/10973/22256. They did a plot from 01797 to 01932 on p.6 which looks pretty similar: it's about 100 in 01797 and also 100 in 01932. It is indeed 79–85 in 01891. At the end of 01776 in their data table (p. 7) it was 86; at the end of the data table in 01932 (p. 10) it was 95.

So we could say that the average inflation rate from 01776 to 01932 was 0.06% yearly ((95/86)*(1/(1932-1776))). But this is probably overstating the secular inflation rate and is better understood as random noise; at the end of 01920 it was 226 (13% higher than the 202 at the end of 01919, close enough to the 15.6% you quote) and in 01894 it was 70. The same calculation thus gives us an average inflation rate of -0.17% yearly from 01776 to 01894 (that is, 0.17% deflation) or +0.7% from 01776 to 01920.

Warren and Pearson also include H. M. Stoker's data for the colonial period, even though the title is "Wholesale Prices in the United States, 1797 to 1932". It starts at 58 in January 01720 and rises somewhat steadily until 01776, at the beginning of which it is 75 before reaching 86 at the end of the year. Stoker's suggestion is that prices were lower worldwide during this period "due to the changes in the value of precious metal," presumably due to the Spanish flooding the world with cheap American gold and silver from Potosí and their other colonies.