吞音 rules for Beijing Dialect
I don't suggest you summarise such rules. As a language learner, one of your goals is saying words clearly and accurately. In this way, receivers would completely understand it the first time you say sentences. Similar to New York and London, there are more outsiders living in Beijing than native speakers of Beijing dialect. Thus, Beijing dialect speakers tend to speak standard Putonghua.
If you want to learn swallow 吞音, your rate of speaking has to be as same as a native speaker. Otherwise, it sounds weird if you swallow phonemes when you speak slowly.
I don't think swallow rules are based on particular tones. All of them change to r not h.
After changing, it becomes 轻声/natural tone.
I think 非常, 多少, 还是, 老师, 派出所, 为什么, 不知道 and 但是 are often swallowed. Other words are rarely swallowed nowadays.

非常 fēicháng &gt; fēirang (ráng is at least 2 times faster than cháng, “faster”)
多少 duōshǎo &gt; duōrao (faster)
还是 háishì &gt; háiri (faster)
小车 xiǎo chē (儿化 rather than 吞音）&gt; 小车儿 xiǎo chēr
老师 lǎoshī &gt; lǎori (faster)
派出所 pàichūsuǒ &gt; pàirusuǒ (faster)
不知道 bù zhīdào &gt; bù ridào (faster)
但是 dànshì &gt; dànri