What classifier could predict spam/ham labels for SMS messages better than Naive Bayes?

I have 7000 SMS messages, 6000 ham, 1000 spam. Typical messages are:

Ham: Yo, any way we could pick something up tonight?
Spam: Great News! Call FREEFONE 08006344447 to claim your guaranteed £1000 CASH or £2000 gift.

I want to implement a supervised classifier that would predict the ham/spam label given a new SMS.

The two classifiers have I tried are as follows:

• Simple-predictor, where I count how many elements in the following keywords

   [
      "!", "click", "visit", "reply", "subscribe", "free", "price", "offer",
      "claim code", "charge", "stop", "unlimited", "expires", "£",
      "new voicemail", "cash prize", "special-call"
   ]
  

  are substrings of the (decapitalized) SMS message and predict spam if the count is greater than 1, ham otherwise. The method achieves

  accuracy (correct guesses ratio): 0.9742822966507177
  sensitivity (correct spam guesses ratio): 0.8452380952380952
  

• Bayes (monograms) predictor, where I split the SMS into a tokens list $L = [t_1, t_2, …, t_n]$ (e.g. for the ham message above $L$ would be ['yo', 'any', 'way', ..., 'tonight']), compare the quantities :

  • $s = P(spam) cdot P(t_1 | spam) cdot ldots cdot P(t_n | spam)$,

  • $h = P(ham) cdot P(t_1 | ham) cdot ldots cdot P(t_n | ham)$,

  and predict spam if $s > h$, ham otherwise.

  $P(spam), P(ham), P(token | spam), P(token | ham)$ are estimated from the training data.

  This method achieves

    accuracy: 0.9881889763779528
    sensitivity: 0.9312977099236641
  

  when trained on 4000 messages and tested on the other 3000 messages

What new idea could I try to obtain a classifier with better prediction scores?

Note that I have already tried ‘tuning’ both Simple-predictor (e.g. trying different keywords list, changing the count threshold, etc.) and Bayes predictor (e.g. performance of bigrams predictor is worse due to a limited training set size) to achieve these scores. Now I am looking for a new idea.