What can I, as a resident of Kansas, do to help tighten sex offender laws?

You can tell legislators that a recent statistical analysis of sex
offenders like rapists and pedophiles found that "treatment" is almost
useless.
I cannot find the article, possibly British, but it found that something like 
55% re-offend without treatment and 50% with treatment.
Therefore, these persons have high probability to re-offend (unlike
homiciders) and re-victimizations are not reduced much if "treated".
The only natural treatment is old age.

I can't find the article but some of these UK authors and their
colleagues may be of interest.
Louise Falshaw, Caroline Friendship and Andrew Bates

http://nicic.org/Misc/URLShell.aspx?SRC=Catalog&REFF=http://nicic.org/Library/018535&ID=018535&TYPE=PDF&URL=http://www.homeoffice.gov.uk/rds/pdfs2/r183.pdf

First, I recommend looking carefully at the term sex offender.  Most
such actions lump all sorts of offenses in with the true pedophile
type of offender.

This last fall in the Quad Cities area, to wit Moline, IL, the city
officials were working on a law which would increase the distance a
registered sex offender must live from any school.  Emotionally,
almost everyone likes such an idea, which in the case of Moline would
essentially force all registered sex offenders to leave town.

A local prosecuting attorney told of a case of a man who was sent to
prison for having sex with a young woman, I think she was around 15 or
16 at the time. It was clearly a romantic relationship, but her
parents pressed charges.  Under the law, this was treated almost the
same as a case which involves rape of a five year old, which is a bit
preposterous.

After his time was served, of course he had to register, but by this
time she was an adult, so they married and have produced several
children. He goes to work every day to support those kids. Under this
law, he will be forced to move his family out of town which will do
absolutely nothing to make things safer for children. For his
children, it will be a hardship.

Because of all the publicity about pedophiles, and the murder cases
they get into, most people think instantly "murderous pedophile" when
the term sex offender is used.  I guarantee if we don't start using
common sense, we are going to have a mess on our hands as often
happens when we go to extreme lengths because of a specific problem,
when we lump all sorts of things into the law.

You pose an excellent question. What I, as a two-decade member of law
enforcement, recommend you do is to beat, bang and kick on your
legislators' doors until they actively pursue creating a nationwide
database of all sex offenders in the US and make it accessible and
searchable to all citizens online. Currently there is no such database
and any child rapist from Texas, for example, could move right next
door to you in Kansas without any fear of discovery. Last year in Iowa
alone, a relatively sedate state by anyone's standards, it was
determined that more than 6000 convicted sex offenders were
unaccounted for. Just image who many there are nationwide. Where are
they? Simple, they've quietly blended in with societyy and they are
living and working near you. A Nationwide database would stop this
ignorant oversight and neglegence on the part of state government and
parole/probation authorities.

What can you do? Lobby, man....lobby hard and lobby like your kid's
life depends on it. Make it your new obsession. Worry your elected
officials to death about A SINGLE, PUBLICLY SEARCHABLE, CENTRAL SEX
OFFENDER DATABASE THAT CONTAINS THE NAMES AND PHOTOS OF SEX OFFENDERS
IN ALL 50 US STATES and make it clear to them that if they don't
listen to you about this they should start looking for a new job
because you're only going to vote for the candidate who "will" listen
and who "will" make this happen.

Good luck;
tutuzdad-ga