I will try to provide an answer from Romania's perspective which has one of the largest communities of Roma people: ~850000. It might also explain, at least in part, Bulgaria's issues in integrating Roma people.
So, I will cover the final question, since it is more answerable:
Why don't the Central/Eastern European countries use their [countries
where the Roma have integrated into local society] experience?
First, it is important to understand that most of people in Romania are Romanians, not Romani. Of course, this resemblance creates confusion and some argued that they should be named "Țigani":
In 2009-2010, a media campaign followed by a parliamentarian
initiative asked the Romanian Parliament to accept a proposal to
change back the official name of country's Roma (adopted in 2000) to
Țigan (Gypsy), the traditional and colloquial Romanian name for
Romani, in order to avoid the possible confusion among the
international community between the words Roma — which refers to the
Romani ethnic minority — and Romania. The Romanian government
supported the move on the grounds that many countries in the European
Union use a variation of the word Țigan to refer to their Gypsy
populations. The Romanian upper house, Senate, rejected the proposal
However, this is considered a pejorative term and one using it in an official discourse (TV, radio, newspaper) can be subject to fines from National Council for Combating Discrimination.
Coming back to the question at hand, the problem is really complex. Historically, Romani were slaves in Romania before 1856 and subject to deportation under Romanian fascist government of Ion Antonescu (WWII).
I do not know about other countries experience in integrating Romani people, but locally there are many issues that make their integration hard to obtain:
- discrimination: Roma people face a great discrimination as mentioned in the Wikipedia article. This makes integration programs harder to implement (e.g. think about parents not agreeing their children having Roma colleagues):
A 2000 EU report about Romani said that in Romania… the continued high
levels of discrimination are a serious concern.. and progress has been
limited to programmes aimed at improving access to education.
A survey of the Pro Democraţia association in Romania revealed that
94% of the questioned persons believe that the Romanian citizenship
should be revoked to the ethnic Roms who commit crimes abroad.
- corruption: EU and other political actors allocated funds to help with Roma integration, but there are serious issues about how these funds were used:
Parliamentarians Madalin Voicu and Nicolae Paun are under investigation along with 10 other suspects for an array of financial offenses relating to the alleged misuse of European Union (EU) funds intended to help the minority Roma population.
As a side note, Madalin Voicu also had a very controversial political discourse about Romani people in Romania.
This article emphasizes the problem:
GERMANY is trying to seize billions of pounds from Romania and
Bulgaria meant for the Roma community after claiming they do not use
Joachim Stamp, integration minister for Germany's largest state, North
Rhine Westphalia, said he finds it "extremely annoying" the two
eastern European countries refuse to use funds from the European
Social Fund (ESF) for its proper use.
- cultural differences: many people perceive that there is great (and unsolvable) cultural gap between Roma and themselves. One particular example is early age marriage (below age of consent).
As a conclusion, Roma's integration heavily depends on the context (use the funds properly, how the others perceive them and are willing to accept that they can indeed be integrated) and "other countries" experience might not be relevant.