The answer to your question is no, there are no other points with numerator or denominator of $5$ digits or less.
If you have access to a Linux system, you may want to try Michael Stoll's "ratpoints", which can be found here. The documentation for ratpoints, and a description of the algorithm is here. This program tries to find all rational points within a given height bound on a hyperelliptic curve in the most efficient way possible.
Otherwise, ratpoints can be accessed through Sage. In the Sage command line, type
from sage.libs.ratpoints import ratpoints
Then,
ratpoints([$a_0$,$a_1$,$a_2$,...,$a_n$], H, verbose=False, max=0)
finds all the rational points on $y^2=a_0+a_1x+\cdots+a_nx^n$, where H is the bound for the denominator and the absolute value of the numerator of the x-coordinate. When I type,
ratpoints([-7^7,14755570,-890273,23328],10000000)
the answer is
[(1, 0, 0), (58, 49109, 1), (58, -49109, 1), (5170922, 1182208159673289, 344763), (5170922, -1182208159673289, 344763)]
meaning that after $\pm P =(58,\pm 49109)$ the next point with lowest height is
$\pm Q =\left(\frac{5170922}{344763} , \pm \frac{387482189339}{38958219}\right),$
and there are no other points (other than $\pm P$ or $\pm Q$) such that the $x$ coordinate has a numerator (in absolute value) or denominator less than $10^7$.